I cannot sing the praises of London enough. You may have noticed that I haven't said anything about the math yet. As for lectures, my friends have had varying experiences with Harvard math professors. You will apply to the Board of Graduate Studies, but you'll list two colleges you most want to get into. I suggest naming Trinity and St. John's, because they are the richest.
Money is a big issue.
There are very few awards for American students from Cambridge or the UK govt. I could go on about all the cool stuff here at Cambridge, but my wrists are hurting.