ANTIQUES

"The World's Best Antique Markets" is the bold promise of Grays, where 250 dealers offer assorted bric-a-brac, memorabilia and quality antiques from £25 up. Monday-Friday 10 am to 6 pm. 1-7 Davies Mews and 58 Davies St., W1, phone 629-7034.

Alfie's has 350 stands in a permanent covered market often frequented by dealers. Tuesday-Saturday 10 am to 6 pm. 13-25 Church St., off Marylebone, phone 723-6066.

Chelsea Antiques Market is big and busy, with clocks, watches, books and bric-a-brac. Monday-Saturday 10 am to 6 pm, 245-253 Kings Rd., Chelsea, phone 352-5689.

BEST DEPARTMENT STORES

With the exception of Marks and Spencer, London's department stores accept major credit cards. Some department stores are open on Sunday, particularly during the pre-Christmas season.

Exclusive Knightsbridge is a good place to start, where Harrods has more than 60 departments for fashion alone. Almost every quality provision is available, and the marble-floored food hall is worth a look just for the experience. Monday-Tuesday 10 am to 6 pm, Wednesday-Friday 10 am to 7 pm, Saturday 10 am to 6 pm. Knightsbridge SW1, phone 730-1234.

Harvey Nichols sells stylish international clothing, home furnishings and household goods. Monday-Friday 10 am to 8 pm (Wednesday and Saturday 10 am to 6 pm only), Sunday noon to 5 pm. Knightsbridge, phone 235-5000.

Farther out is Barkers, an art-deco building resembling an ocean liner, with fashion and household-goods departments. Open Monday-Wednesday and Friday 10 am to 6:30 pm, Thursday 10 am to 7 pm, Saturday 9:30 am to 6 pm. 63 Kensington High St., phone 937-5432.

At Piccadilly is the prestigious Fortnum and Mason, purveyors of quality goods to customers at home and abroad. Wander in from the street and savor the rich aromas of the exotic coffee department. Monday-Saturday 9:30 am to 6 pm. 181 Piccadilly, phone 743-8040.

Close by are the Piccadilly and Burlington arcades, lined with small luxury stores. Lillywhites has five floors of sportswear. Open Monday-Friday 9:30 am to 7 pm, Saturday 9:30 am to 6 pm, 24-36 Regent St., phone 915-4000.

Oxford Street is now colonized by cheap clothing and music stores, but some outstanding department stores remain. Selfridges offers cafes and restaurants besides a vast array of clothing and goods departments. Monday-Wednesday and Friday-Saturday 9:30 am to 7 pm, Thursday 9:30 am to 8 pm. 400 Oxford St., phone 629-1234.

Along the road is Marks and Spencer, renowned for its no-nonsense approach to clothing, accessories, home furnishings and food. No credit cards. Monday-Wednesday and Saturday 9 am to 7 pm, Thursday-Friday 9 am to 8 pm. 458 Oxford St., phone 935-7954.

John Lewis, "Never Knowingly Undersold," offers one of the largest fabric departments in Europe and everything else from carpets to jewelry. No credit cards. Monday-Wednesday and Friday 9:30 am to 6 pm, Thursday 10 am to 8 pm. At 278-306 Oxford St., phone 629-7711.

Liberty specializes in dress fabrics, but also sells furniture and gifts. Fine mock-Tudor building with traditional interiors. Monday, Wednesday, Friday and Saturday 10 am to 6:30 pm; Wednesday 10 am to 6 pm, Thursday 10 am to 7:30 pm. 210-220 Regent St., phone 734-1234.

BOOKSTORES

At Charing Cross Road, between Leicester Square and the Tottenham Court Road subway station, you'll find dozens of bookshops -- new, secondhand and antiquarian. Nearby Cecil Court is a haven for the antiquarian sleuth: P. J. Hilton, open Monday-Friday 9:30 am to 7:30 pm, Saturday 10:30 am to 7:30 pm. 12-14 Cecil Court, WC2, phone 379-9825. You'll also find good bookstores quite close to the London University campus at Gower Street. Dillon's covers every possible subject in paperback and hardback. Monday and Wednesday-Friday 9 am to 7 pm, Tuesday 9:30 am to 7 pm, Saturday 9:30 to 6 pm, Sunday noon to 6 pm. 82 Gower St., W1, phone 636-1577. Also at Trafalgar Square, phone 839-4411.

London's largest bookstore is Foyles (which is often messy and involves a time-consuming payment system). Monday-Saturday 9 am to 6 pm, Thursday 9 am to 7 pm. 119-125 Charing Cross Road, phone 437-5660.

Waterstone's is an efficient place with well-informed staff. Monday-Saturday 9:30 to 8 pm, Sunday noon to 6 pm. 127-129 Charing Cross Rd., WC2, phone 434-4291, and 193 Kensington High St., W8, phone 937-8432.

FACTORY OUTLETS

Factory outlets sell last year's fashions at half price or less. Most are outside London, so plan to visit them by taxi.

For those eager to sample the best, we recommend a day trip to Oxfordshire. The Bicester Outlet Shopping Village houses 48 discount shops, including the pricey Jaeger, Kurt Geiger and Aquasculum, and those high-street names Benetton and Jigsaw. 50 Pringle Drive, Bicester, Oxon (about an hour and a half distant), phone 01869-373-200.

Burberry sells famous-name raincoats and accessories. Monday-Friday noon to 6 pm, Saturday 9 am to 3 pm at its discount outlet at 29 Chatham Place, Hackney E9, phone (0181) 985-3344.

Nicole Farhi and the French Connection is a tiny workshop specializing in stylish, inexpensive ladies' and men's wear; phone to check stock. Tuesday-Wednesday and Saturday 10 am to 3 pm, Thursday 11 am to 6:30 pm, Friday 10 am to 5:30 pm. 75-83 Fairfield Rd., Bow E3, phone (0181) 981-3931.

MALLS

Most London suburbs have their own mall or commercial center. The Big One is Brent Cross, at the junction of the North Circular Rd. and the M1 motorway. Monday-Friday 10 am to 8 pm, Saturday 9 am to 6 pm.

In central London there are small shopping centers at The Colonnade Walk, a bright and airy space around a central fountain. It's at 123-151 Buckingham Palace Rd. Victoria Place has many small stores. Open daily 9 am to 8 pm at 115 Buckingham Palace Rd., phone 931-8811.

The Arches is an intriguing specialist shopping nucleus, well fashioned from Victorian arches beneath Charing Cross Station. Villiers Street.

MARKETS

Of the dozens of street markets held in London and its boroughs, here are three of the more popular:

Portobello Road, with antiques on Saturday, general goods Monday-Saturday, flea market Friday and Saturday. Monday, Wednesday, Friday, Saturday 7 am to 5 pm, Thursday 9 am to 1 pm. Portobello Road, Golborne Road and Colville Terrace, Notting Hill.

Berwick Street, offering clothing, food and household goods Monday-Saturday; best time is midday. Mayfair.

The artsy canal-side market at Camden Lock makes a pleasing side trip for its wide variety of crafts, clothing and bric-a-brac. Open all week, with antiques sold at Camden Passage on Wednesdays 10 am to 2 pm, Saturday 10 am to 4 pm. Islington High Street, northeast of center.

Brick Lane, scene of a lively Bengali market on Sunday 6 am to 1 pm. Huge variety of clothing and exotic foods. Brick Lane, Spitalfields E7.

TRENDY SHOPPING AREAS

For a smarter and less hectic alternative to Oxford Street, consider Kensington High Street, a few miles to the west. It has a range of national chain stores, together with more specialized boutiques and shops.

Camden Town, just north of center, is popular for imported records, pine furniture and poking around individual stores for something different in clothing.

Tops for trendiness, however, is Covent Garden, conveniently located between the West End and the City. A former fruit and vegetable market centered on the first planned piazza in London, this revitalized hot spot has attractions of every sort, including imaginative street entertainment (licensed), variegated bars and pubs, exotic eateries and arcades of craft and modern jewelry shops, boutiques and market stalls. Phone 836-9136. At Covent Garden underground stop on the Piccadilly line. Although Chelsea's Carnaby Street has lost much of its novelty since its 1960s heyday, Kings Road in Chelsea is still a place for the hip to be seen, browsing boutiques or grazing in cafes.

UNIQUE OR UNUSUAL

The Soho area, just north of Piccadilly Circus, has a reputation for seediness but is recently much improved. Asian supermarkets and highly individual delicatessens have survived alongside briskly modern sandwich bars and designer clothing shops.

For traditional custom tailoring (menswear), Saville Row, Mayfair, is tops.

The Salvage Shop sells merchandise from bankrupt merchants as well as fire- or flood-damaged goods at discounts of up to 50%. A great place for rummaging. Stocks anything from perfume to clothespins to typewriters, but specializes in furniture. Monday-Saturday 9 am to 5:30 pm. 34-38 Watling Ave., Brent Oak, Edgware HA8 OLR, phone 952-4353.

David Richard & Sons are silverware wholesalers who also sell to visitors at knockdown prices. Monday-Thursday 9:30 am to 5:30 pm, Friday 9:30 am to 4 pm. 12 New Cavendish St., Mayfair, phone 935-3206.

London is particularly well blessed with antique and art auctioneers: Bonhams, at Montpelier Galleries, Montpelier St. SW7, phone 584-9161; Christie's, 8 King St. SW1, phone 839-9060; Sotheby's, 34-35 New Bond St. W1, phone 493-8080.

R. Twining & Co. is 290 years old and dedicated to the famous family of tea shippers. It's half tea shop, half museum. Monday-Friday 9:30 am to 4:30 pm. 216 Strand, WC2R 1AP, phone 353-3511.

Charbonnel & Walker. Established over 120 years, this shop sells traditional chocolates and exquisite novelty confections. Open Monday-Friday 9 am to 6 pm, Saturday 10 am to 5:30 pm. 1 The Royal Arcade, 28 Old Bond St., phone 491-0939.

Best of British purveys traditional British crafts. Monday-Saturday 10:30 am to 7 pm, Sunday 1 to 5 pm. 24 Thomas Neal Centre, Earlham Street, phone 379-4097.