The country is divided because a very divisive referendum campaign, with misrepresentations or downright lies propagated by both sides, yielded a result that was split almost down the middle. It is not undemocratic to try to get a disastrous decision reversed.
No, it’s not. But for the majority, it was not a disastrous decision.

Ever since Maggie’s days we’ve been the pain in the arse standing outside pissing in, getting rebates, not joining the euro or Schengen and demanding all sorts of other exemptions.
Not quite, it was in ‘Maggie’s days’ that we got the rebate agreed.
Since that time Tony Blair conceded part of the rebate in exchange for a promise of a review of the CAP, which was never forthcoming, but the EU retained the benefit of the reduced rebate.

The EU has been taking advantage of UK for almost 50 years. It is hard for them to give that up.