What kind of antiques were you looking for? Vintage at all? Sometimes you can find things mingling with each other. I found a 100 year old mesh purse in a Retro shop so you never know!
I just found Alfies Antique Market yesterday. Definitely worth a visit. They have a website too. Easy walk from Marylebone tube. Open Tues-Sat. Great rooftop cafe at VERY reasonable prices. The people opposite us had two meals and two bottles of wine for £30!
Gray's Antiques Market just near the main Oxford Street shopping district near Bond Street tube. It is open during the week and Saturday. I've seen it from the street and is next on my list to explore.
London Silver Vaults in The City makes a good visit too.
Greenwich Market on the weekends has a small market near the cinema with antiques and vintage items.
Spittalfields and all the markets on and around Brick Lane are good. Sundays are my favorite day for vintage.
Mondays are antique days at Covent Garden
There are lots of vintage only shops and charity shops to browse too. Car boots or small hall fairs are good choices too but can be tricky to find because they are not widely advertized
Nowhere near London, Hay-on-Wye is the place for old books and antiques. I have a lot of favorites outside of London too. Wales also has many antique shops.
Edinburgh has lots to browse too. I mainly went charity shopping last time I went.
Have fun!