London does not have to be that expensive. Have a look at
www.wherecanwego.com and enter details for London and then click free things only and all sorts of stuff comes up - Depending on how adventurous you are..Help the aged are looking for people who are interested in doing free skydives for charity
also there are cheap hotels
www.easyhotel.co.uk ( might be easyhotels ) and we recently went to a Chemical Brothers Concert and stayed at a hotel in Earls Court right next top the tube station called Exhibition Court Hotel 4 - it was 50 quid a room rather than per person. I emphasise NOT somewhere for a romantic weekend! but if you want somewhere clean to crash..then its ok..very groovy...old bed throws but the bed linen and sheets themselves are crispy white a clean. Bathroom was clean too.
Stay away from hotels that are just called Hotel 60, Hotel 88 ect - They are hovels and they stink..their pictures look fab and the prices are cheap..but seriously they are rotten. At least with Exhibition Court Hotel 4 you get what you see....Old fashioned and groovy but CLEAN!
Also all the museums are free in London and I believe you can do a rice boat trip for about 7 quid down the thames.
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On a side note other than London, what about camping on the coast or renting a little holiday cottage for a week? Chill out and have girlie time.