Most commercial wine, beer and cider is filtered using animal bi-products which include fish bladders (isinglass), egg albumen & bone charcoal among other things. If you go into a pub in London chances are the staff won't know which drinks are suitable for vegans.
To check if your wine or beer or cider is suitable for vegans visit Barnivore.com

The Spread Eagle
London's first 100% vegan pub, located in Homerton, East London. All food and drink is vegan . The food is provided by Club Mexicana. www.thespreadeaglelondon.co.uk/

The Queens Head 
This Brixton pub went vegan early 2019 and not only has a good selection of vegan drinks but also is home to vegan pizzeria  PickyWops
www.queensheadbrixton.co.uk/

Karamel
This bar/club/restaurant/music venue in Wood Green in North London is 100% vegan. Vegan wine and beer is available. The venue is also the location of the monthly London Vegan Drinks. Visit the Karamel website http://karamelrestaurant.com/

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Pubs
Want to have vegan beer or cider in a traditional London pub?
Then visit one of the Sam Smith Pubs as they all sell vegan beer and cider. Their website states:
All Samuel Smith’s beers and ciders are suitable for a vegan diet (except cask conditioned Old Brewery Bitter and bottled Yorkshire Stingo).
A list of all their London pubs can be found by clicking on this link.

Alternatively Brewdog Bars serve Vegan Society trademarked beers and lagers

It is unlikely you'll find vegan wine in a pub.

Restaurants
Some of London's vegan & vegetarian restaurants are licensed and serve wine and beer that's suitable for vegans. These include 222 Vegan Cuisine, Vantra Loungevity, Purezza, Tibits, Manna, The Gate and a few others.

Supermarkets
Of the major supermarkets, Marks & Spencer, The Co-Op, and Sainsbury's label which wines are suitable for vegans.

Buy Online
Vegan wines can also be purchased online from Vegan Wines Online and from Vegantipples.co.uk  
The organic wine company Vintage Roots also have a selection of vegan wines

To check if your wine or beer or cider is suitable for vegans visit Barnivore.com or download the VegeTipple app