This would not be undemocratic. The whole difference between autocracy or dictatorship and democracy is that in democracy you have the right to change your mind. In general and local elections throughout the democratic world, the process of a re-vote is mandatory every few years, as it is in the UK.
The 2017 Brexit referendum was unique for several reasons. The facts behind the offer were more or less unknown and both sides used campaign techniques which were misleading. People were led to believe the project was simple, when in fact it is so complicated nobody seems to be able to get a grip of it. Leave constantly pedaled misleading data to show how much more money would pile into services if we left and immigration would be drastically cut. Moreover the overall message was everybody would be better off. The truth is now clear, whatever side you are on. A soft Brexit will leave us worse off for years if not forever, a hard Brexit much worse off and a crash Brexit so much worse off that it will amount to an economic crisis.
In the campaign the Remainers exaggerated the immediate consequences of voting to leave, but the Leave campaigns talked up the gains if we did. Finally, on something so fundamental to the future of the rising generation, a huge majority of whom voted to remain, there should have been at least a 60% threshold to leave. And there was not. So the country is split apart.
It is very much in order to talk of a second vote and very democratic to do so. If Labour decides to adopt support for the second referendum at its party conference it will put into the mainstream what the majority of its own members and, according to the polls, the country wants. When the beleaguered May, isolated in Downing Street from just about everybody, cries that she is carrying out ‘the will of the people‘ it is not unreasonable to demand that she finds out what that actually is.