My recommendations for London are:
Knightsbridge, Belgravia, Chelsea area:
Harrods - by far the best high-end menswear store in London.
- There are various shops around harrods (inc. Church's, Rolex, and a Corthay boutique a little south), as well as another large department store called Harvey Nichols.
Sloane Street - luxury superbrands like Gucci, LV, etc., as well as Loro Piania and Cucinelli.
King's Road - famous road that used to be a hotspot for artists/writers (Wilde, Whistler), then aristocrats, then rockstars. Not so interesting for menswear enthusiasts any more.
Mayfair / St James's area:
Bond Street - every major luxury brand has its flagship on or nearby the street
- Brioni is on Bruton Street
- John Smedley on Brook Street (English knitwear)
- Kiton and Drake's are on Cork Street (connects Bond Street to Savile Row)
- Cucinelli and Ede and Ravenscroft (and A&F!) are on Old Burlington Street.
- Burlington Arcade (C&J, Harry's, Globetrotter, lots of small luxury shops) and Savile Row both run off OB Street.
Mount Street - very cool stealth-wealth street in Mayfair. Stores include: Double RL, Goyard (luxury luggage, trunks), and Rubinacci.
Jermyn Street - Edward Green, John Lobb (Hérmes), C&J x2, Church's, T&A, H&H, etc.; Emma Willis and Emmett are two shirt-shops unique to London that provide an OK shirt for £100 roughly.
St. James's Street - SAB, Jonh Lobb (English, bespoke only), Gentleman's Clubs, etc.
That's where I shop in London.