It would empower the right in the long run. Just imagine the uproar from the right, if the "ELITES ignored the referendum voted on by the common people". It would be a right wing bonanza for years to come.
A Conservative prime minister and government granted the referendum and right wing populists took the ball and ran with it and won democratically.
Those who supported Remain need to accept that the right won the referendum and move on expeditiously to implement it. In reality I don't think there are any Labour or other liberal politicians who are supporting a second vote.
If things work out for the UK, then the Right was right, so to speak. If things go badly, perhaps in 10 years or a generation they can revisit this. Some of the older supporters of Leave will have died off and the younger supporters of Remain will still be around - unless they change their minds as they age. 
To ignore the referendum or hold a re-vote right away, while I sympathize with the sentiment behind the ideas, would only serve to make the right even stronger.
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