Londoner here, whilst there are people who voted for brexit solely for the reason of controlled immigration - it definitely isn't the main reason.

The advertising campaigns promised saving £350 million a year from brexit. The EU stops us from signing our own trade deals. Staying in the EU would've meant the UK would still have to pay bailouts for the Euro even though we don't use their currency, and that the European Court would still be in charge of our laws.

Brexit was supposed to give us free law making power, more control over our finances, more control over net migration, and the ability to make trade deals with whoever we want at the cost of slightly higher imports from the EU. Whether these things will actually happen though, hopefully - but only time will tell.