wow you guys are aficionados! Looks like you've seen the big sights and the more secret sights too, inc South Bank!
Do check out Tate even if you don't like the exhibits - the architecture, atmosphere and people watching is often much more interesting than the art which is a fun sideshow in itself (try and find the worst piece you can, and the best, most pretentious one to put by your chaise longue at the after party - it may be the same - plus the one you genuinely like).
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Unlike the other hotspots Peckham is not obviously hipster when you arrive, it feels 'real' aka sketchy and poor (though it isn't), with a super-interesting vibe of South London chav, African markets, thrift stores, indentured artists, Euro tourists, Euro immigrants, and in-yer-face Jamaican bounce. One of the pleasures is actually trying to find the buildings (Bussey and Levels) and the kooky way through alleyways and carparks. Also a big amount of high end foodie stuff going on, and cinema for a fiver. Don't expect it to be as obvious as Brick Lane market or manicured like Hoxton, and definitely weekends> weekdays.
The other big parks are Hampstead Heath (prettiness and views) and Richmond Park (wilderness with deer) which are HUGE spaces.
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Oh and Kew Gardens for the world's best, and the latest UNESCO Word Heritage Site.
https://secretldn.com
It sounds like you've done so much it'll be time to head out again, into the metro.
Daytrippers - hire a car and head for Cotswolds for quintessential pretty England, inundated with other daytrippers
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Oxford (genuinely working town despite the droves) over Cambridge (utterly given over to plugging the tourist).
www.adventureballoons.co.uk
If you visit in warmer climes, Brighton - head for the Lanes medieval warren of alleyways, and North Laine (unconnected), an area of everything kooky and leftfield. The beach is pebbly and a vast show of the great unwashed here to take their first dip. A bit like Vegas by sea where everyone loses. Try not to take photos of the freaks. Kemptown (aka Camp town is the gay high street for older queers with spin-offs in the sidestreets).
Margate is the smaller, sketchier, hipper, artsier, tackier, tongue-n-cheek-tackier version
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