Hey There,
If you are in barbican then Gutshot is definitely your best bet as it is litterally just a few minutes from you - My advice regarding membership is give them a call and find out what the exact rules are at the moment because I am sure you will be ok - There number is listed here
http://www.londonpokerdirectory.com/index.php/Venues/gut-shot-poker-club.html. And yes they do have a .25/.25 game although it is normally made into a .25/.50 game by the players.
You can also always get a cash game down at The Vic and to be honest these are likely to start earlier as the ones at the Gutshot don't normally start until people start dropping out of the tournament. However it is a bit more of a mission to get there Details on The Vic are here
http://www.londonpokerdirectory.com/index.php/Venues/vic-poker-club.html
Finally - Cash games don't really happen (officially) in pubs but there is one just 5 - 10 mins walk from the Barbican on a Tuesday night at the same time as a £5 tourney and a free play beginners tourney - They talk about it on the site butit should be happening - Contact Blapo to check - It is small stakes like .25/.25 blapo.co.uk/the_tuesday_game__clerkenwell_house.html