Where to start ...
The EU has an open borders policy. There is nothing to stop anyone from the 28 EU countries from turning up in the UK. There is a perception that these immigrants take jobs from British people, and squeeze them out of getting their kids into local schools, add to hospital waiting lists etc.
There is a further concern that the EU will keep getting bigger, and in a few years anyone from fuckknowswhereistan can rock up on top of the current 28 there is now.
The UK ships £350m a week to the EU, and we don't get much of it back.
More and more law is being controlled by Brussels (the EU parliament). Not all of it is terrible, but they haven't helped themselves by introducing some daft stuff over the years.
More and more regulation is coming out of Brussels. It's never ending and a lot of it is bollocks.
People want to poke the politicians in the eye.
Oh, and a lot of people are stupid. And a bit xenophobic.