The Brits have said numerous times that they do not want and will not build a hard border in Northern Ireland. It’s the EU that is insisting on it due to their fear of goods flowing from the UK into the EU.
As for the referendum, it was promised for years and all parties in the UK swore IN ADVANCE to abide by the decision of the British people. They are free to break their word if they want.....but I suspect there will be severe electoral consequences for years and years to come for any political party which does.
The EU isn't insisting on the hard border. It was the UK who gave the suggestion that the RoI put in passport checks on entry - thereby annexing RoI to the UK. The RoI rejected that, so the UK wants a border to keep out those pesky EU migrants.