Only a couple left now
@Jwebb90 im sorry to say. Seegars & Snuff in Covent Garden or Fox's on St. James. They'd be about your best bet. Just be aware the selection of both pipes & tobacco might be somewhat dissapointing & nearly twice the price of what you'd pay online.
If you're thinking of stocking up on certain things, you'd be wiser to order online & get it delivered to your hotel. Fox's is still a must visit though, a downstairs museum & a rather nice smoking lounge upstairs. Also, if you're looking for a nice hat 'Lockes Hatters' is only a couple of doors up from fox's & is worth popping in for a look.
Best online vendors in the UK are;
Mysmokingshop
James Barber
The Black Swan / ye olde baccy shop
GQ
You can ring any of those up & pay over the phone if you'd prefer & get it delivered the next day.