I was one of the people working at this election in a London Borough.
We were open from 7am until 10pm, and the Polling Stations are all very local to the registered address of the voter so public transport is not required. Add to this the fact that if you were disabbled you can almost bet that one of the local parties would have been willing to give you a lift if they thouht you might vote for them there is no excuse not to get there on time. The staff were there from 6:15am until about 10:30pm and unable to leave the station or take any proper breaks unless things got quiet.
At our location we had about 5k people on the voter lists, this list was then split into three parts. So after the postal votes etc each station probably had about 1500 people to look after. We had papers for about 1200 people at each station, we could have got more if we needed them but it's very unlikely. Everyone wants us to stop wasting money and printing papers for every voter would mean an extra 30-40% of paper being paid for and wasted.
People have to go to the particular station and be marked off their list to ensure that they only vote once, so there is no way we could just add extra staff once we had started. Most of the day we had 30-40 people delt with each hour, at our peak 6-8pm we were dealing with 100 per hour (I logged the number every hour), and queues were stretching out the door but we were working as fast as possible. the voter cards made our life much easier because we could use the number to go straight to the place on the register instead of having to look it up via street name, house number and name.
We didn't have to turn anyone away for being late, but most elections we end up with someone that seems to want to see how fine they can cut it and still vote. The rules we were working to were if you have a Ballot Paper at 10pm you can vote but we will not issue any papers after 10pm.
I've seen a lot of posts/comments all over the place sugesting the use of computers for doing the lists so people can vote anywhere they like. The problem with this is that most of the voting is done for a particular Ward so the papers would need to be kept together in that ward for counting etc. If you moved the whole thing to an electronic system I think we'd have even more problems than we do now and more claims of tampering with the systems.
The great thing about the current UK way of voting is that there is a true paper trail that can be looked over later to see what happened and we don't require electricity to set a station up. If the only location available is a portacabin we can use that, there have also been ocassions where the start of the poll has been run from the back of a car due to keyholders not turning up.
The UK system might not be perfect but it's robust and for the most part it works well.