Quick answer: In Hounslow you can play board games at London Games Club at Riverside Vineyard Church (Meetup group), London Games Club at The Town Wharf (Meetup group) and West London Tabletop at the Tabard (Meetup group). The next confirmed date is Fri 13 Nov, 7 pm (London Games Club at Riverside Vineyard Church).
Hounslow has three weekly board game sessions. West London Tabletop plays every Saturday afternoon at the Tabard in Chiswick, the Isleworth Boardgamers from London Games Club play strategy games all day on Wednesdays at The Town Wharf on Swan Street, and on Friday evenings there's a games night at Riverside Vineyard Church in Feltham. Twickenham is next door, with more nights.
3 × Meetup group
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A Friday board games night in Room G14 at Riverside Vineyard Church in Feltham, from 7pm to around 9:30pm. Use the main entrance. The hosts keep a list of their games and bring a selection each week, and you can ask them to bring something in particular.
Where
Riverside Vineyard Church, Air Park Way, Feltham, TW13 7LX
The Isleworth Boardgamers play all day every Wednesday, from 11am until late, in the top-floor room at The Town Wharf on Swan Street (they moved here from The London Apprentice). It's an established group that suits people who already play strategy games regularly, think Great Western Trail, Ark Nova and SETI, but newcomers are welcome. Come and go as you like.
West London Tabletop Gaming and Good Food runs a Saturday afternoon board games session at the Tabard in Chiswick every week. It's a big group, with nearly 3,000 members on Meetup, and the same organisers run weekly board game evenings and riichi mahjong sessions elsewhere in west London. RSVP on Meetup to see the details.