The UK is just weird about that.
Decades of hooliganism (mostly a thing of the past thankfully) has meant that you can't be in possession of alcohol within view of the pitch in the top 5 tiers in the UK. (And by the 5th tier you're looking at matches that have attendances anywhere down to 400 or so, although some clubs in the 5th tier still manage to attract 10000 fans to home games).
This spills out into the local community around stadiums too. Many pubs really close to the ground will have extra restrictions on matchdays, that's probably what you've experienced. But that's not just the UK, I remember going to a River Plate game in Buenos Aires 20 years ago and being amazed that on match days there was no alcohol served within a mile of the stadium or some such rule.
I've been to Champions League games in the UK sponsored by a variety of alcoholic drink companies and they weren't serving alcohol anywhere in the stadium (well, I guess they still do in the hospitality sections).
Even when the stadiums do serve alcohol they do strange things like stopping serving as the second half kicks off. As someone who wants to watch all of the football I've paid to go see it's a very odd thing getting a pint at half time and drinking it in under 10 minutes in order to be back to the stands in time for the second half to kick off. Us Brits just accept it and deal with it.
Compare that to watching rugby or cricket in the UK where you have no fan segregation and alcohol allowed at the seats.
It's also much more relaxed at the lower tiers of UK football. I've watched a few Dulwich Hamlet games with a friend and they allow to bring your own beers in (may have changed, haven't been for a few years), and sometimes have a "pay what you want" admission price.
Wherever I go in the UK I try and keep a look out for a local game, even if the football is terrible the people watching is often amazing and worth the admission price alone.