I have no idea of British politics, but I don’t see how Brexit is stopped by a change of parliament control, without a change of law as well. The date was set months ago. Hard Brexit happens. I think the controversy is how to enact a May like Brexit deal.
The UK doesn't have a written constitution, but the one fundamental principle of British government is "Parliamentary sovereignty." Parliament can do, literally, anything, and one Parliament can overrule a prior one. The referendum was technically non-biding, although most politicians said they would abide by it, because it was a vote of the people, not of Parliament.