Well... dont, because you'll just be disappointed that it isn't the same London we show to foreigners in books. And don't expect it to feel English either, you need to see our rural communities to get a sense of that. But a trip to London ought to be cheaper than going to Africa and Pakistan and Poland I suppose, you'll experience rootless and degraded versions of a lot of the worlds cultures if you visit London...
But whatever you do, just stay away from Manchester and Liverpool, or you'll wish you never came here... Those cities would be diagnosed with Narcissistic Personality Disorder if they were people, instead of cities that are breeding grounds for lowlife. Nothing good has come out of Manchester since the very early (pre-rave) 90s, and nothing of note from Liverpool since the Beatles in the 1960s, except for an axed television soap about incest and people burying a dead body under their patio. Unbelievably both places, have a tourist industry - don't bother.
Nice places in Britain to visit would be the New Forest, the Peaks and the Lakes, Cornwall's coasts and the Scilly Isles, Norfolk Broads, Yorkshire Dales, Snowdonia, the Scottish Islands and the Highlands of Scotland etc... but there are places that too many people ignore as destinations like the Pembrokeshire coast in Wales and Dumfries and Galloway in southwest Scotland, that are as least as good and you don't need to worry about the tourist season or avoiding tacky tourist traps. I love both of them...