Hi, im from london and would be happy to point you in the right direction.
There are tons of great craft brew pubs. However, wether they are local brews is a different story. They tend to sell a wide selection of fantastic british beers though. You will stumble across a few local products though.
We have a brewdog in soho which is a pretty standard craft beer joint (im sure you’ve heard of them) they do sell some pretty nice beers. There is a place in farringdon called the craft beer company which is great, great selection. Theres also a great place in temple called the temple brew house. Theres also a place called euston tap which i’ve never actually been too but a lot of my friends enjoy it there. We have a beavertown which im sure you’ve heard of, love it there, its on mill mead road. Whenever im in hoxton i always pay a visit to the old fountain, again, nice selection there. Oh yeah and visit stormbird in camberwell! Thats a favourite of pretty much everyone.
To be honest i could list places all day.. those are some good ones that I can think of off the top of my head. Honestly though, you can literally walk around most parts of london and you’ll probably stumple across a pub every few buildings! Wherever you are, just do a quick google search of craft beer near you and im sure something will come up! I usually drink around shoreditch, covent garden, camden areas but theres endless places to visit.
Now, if you want to come a little bit out of london I would highly suggest taking a trip to Marlow. Theres a brewery there called the marlow brewery and it was started by two guys who lost their jobs, started brewing beer, became pros and now supply beer all around the country. They make some fantastic beers, a new one for every month plus some all year rounders. If you go there you can take a tour around their brewery and then sit drinking their beer all day! They have a great shop too and you can get some beer bottled up fresh to take away with you. Marlow isn’t hard to get too. You just need to get to paddington and jump on the train to maidenhead and then from there to marlow. Or you could just jump in a cab. It should only take an hour/ hour and a half id think and their beer doesnt get much more local. I may be wrong but im pretty certain they brew with the local water and use grain grown on the farm next door. Bery traditional brewery, no filtering/ pasturizing.
Shoot me a message if you need to know anything else regarding london.
Hope you enjoy your visit.