There have only ever been 3 national referendums in Britain. One to join the EU, one to leave the EU, and one over Alternative Vote. They used to be considered unconstitutional, a tool for demagogues. I would be happy to ditch them forever.
Heck, we have confirmation dialogs when you close a word document - I don't understand the opposition to having an "are you sure you want to quit?" for brexit.
Brexit is a pretty major decision, and it's not unreasonable to me to require that the majority that voted for it is in fact stable and consistent via holding a second vote. If the second vote does not indicate that a majority supports leaving, that seems like an indication that it was a fantastic idea to hold a second referendum.
We either have a direct democracy, or a representative democracy, not bits of each as suits someone's point. Up until the first EU referendum in the mid 70s they were considered unconstitutional in Britain.
The Bolsheviks also gave fair elections a shot....one shot....one and done.