Yes London has a pub called the Ballot Box, it's on Horsenden Lane between Perivale and North Greenford. Nothing big drives this way thanks to a width restriction at the old bridge over the Grand Union, but the Capital Ring passes by just after its detour up Horsenden Hill so you might have seen it. What's more it's not the first pub of this name on Horsenden Lane and what's more the aforementioned bridge is called Ballot Box Bridge. There is of course a story behind it, and it's because even bargees had to vote somewhere.
The original Ballot Box pub was closer to the foot of the hill, also closer to the canal, in the long lost hamlet of Brabsden Green. This consisted of a few cottages, an orchard, a village shop and a public house, which might seem like over-provision of services in such a rural location but I guess makes more sense when you're quarter of a mile from a seething waterway artery. Built around 1867 the pub was used by bargees as a polling station when needs required, as well as an everyday watering hole, hence it got the name the Ballot Box. I only know this because I was walking past yesterday, just north of Ballot Box Bridge, and found a decaying information board in the woods overlooking the lane.
It says the pub was demolished in 1943 but that a few scraps remain deep in the trees, which must be just behind the board given the scraps of railings I spotted in the undergrowth, but nothing substantial enough to cast a vote in. After I got home I also found a decent copy of the faded photo here, showing it was deemed worthy of gracing a postcard, and also an oil painting here showing it was a Benskins. The rest of the hamlet of Brabsden Green was demolished in the 1970s (unusually for greenspace rather than development) whereas the pub was replaced up the road in more solid 1940s form. Electoral rules no longer required it to be used on polling days but they kept the name which was nice, and possibly the only nice thing about it.
Today the Ballot Box is a Hungry Horse, a chain pub focusing on cheap beers and value food, a few rungs lower than a Beefeater and with less character than a Wetherspoons. This is not necessarily a bad thing, particularly for those prioritising socialising over savouring. But what'll attract some and repel others is the Wacky Warehouse to one side, a softplay zone where toddlers can run riot, indeed a couple of firebrands were dashing in with mummy as I passed by. It's perhaps therefore not the ideal spot to celebrate this election night, not even after all the bouncy kids have gone home, not even with the special Thursday offer of a free dessert, mainly because they close at 11pm before the ballot boxes have been counted.