I was amazed to discover that there is no ID check, even with in-person voting, in the UK. Don't know what it's like in the rest of the first world but I think fraud has always been easy in the US too, mail-in ballots or not.
Like SA, your name needs to be on the voters roll before you're allowed to step up to the polling booth, which means you would've had to register to vote in your area first.
Unlike SA, though, there's no verification to prove you are who you say you are, because like you've correctly stated, there is no requirement for a state-issued ID in the UK, because it apparently infringes on people's rights somehow (they'll refer you to the war, and how people were numbered, etc). Also, they don't mark your thumb or anything as a safety to ensure you don't go back later and vote under someone else's name. It's the UK, after all - the chances of there being more than one John Smith in your borough are freakishly high.