I just came back from London. I shared my 6 days iternery to you.
London is very hot during my stay (E/Jul~B/Aug)
All the museum, train station & bus got no air-conditioned.
We could just a quick look for the museum.
Day 1 Early morning arrival => Hotel Check in
=>Green Park => Buckingham Palace => St. James Park => Westminster Abbey
=> Covent Garden
Day 2 One day Tour to Stonehenge + Bath
Day 3 Oxford + Bicester Village
Day 4 Harry Potter Studio => Natural History Museum => Harrods
Day 5 British Museum => Borough Market => M&M 's world => Les Miserable Musical
Day 6 London Eye + Big Pen (just photo) => London Bridge by Thames Clippers
=> Shopping at Oxford Circus