Kathryn:
I seriously doubt the weather in my home town will be any more cold, grey, dismal and depressing than it is here in Michigan. Dress for a Northern USA climate and you'll be fine.
Expect cloud cover and definitely take a small compact brolly (umbrella!) and rain jacket (waterproofs to me!). Keep these in your back pack at all times. British people never let the weather stop then from going out and doing stuff. I'd pack some jeans and a cardi or two and a winter coat: but I have to tell you, that's exactly what we are all wearing in Michigan where the sun has not shone for a week now. It's really not so different. In fact, British temperatures are never as extreme as they are in the US. London 'aint no Fargo, ND, thank God, and the close, compact nature of the city, thanks to the buildings, keeps it warmer than in the surrrounding countryside.
Where exactly will you be in London? Try and get in some theatre while you are there (the National has a variety of different performances each night), and the National Film Theatre (the NFT) on the South bank (South of the River thames) is the place for non-mainstream, art house and international cinema.
Places to shop and soak in the atmosphere: Covent Garden, Camden, King's Road, Oxford Street, etc.
London, dirty? I don't think so. It's a CITY: don't expect huge pastoral sweeping landscapes! Expect people, crowds, noise, and loads of cultural opportunities.
You have to go on the London Eye on the South bank, a huge ferris wheel affording views over London and along the river. Smashing! Try the National Gallery in Trafalgar Square, the Tate Gallery, perhaps the V & A (Victoria & Albert Museum). What else?
Buy a copy of Time Out from Smiths (W H Smiths, newsagents and confectionary shop) as soon as you get there and it will tell you exhaustively what is on for the full week from movies to transvestite shows, to jazz clubs to La leche Club meetings!!!
What else can I tell you? Have a fabulous time!!!
Clare