At the time of writing this, there is an Online petition requesting a 2nd Referendum, and 2 Million plus have signed it so far.
Now everyone knew the referendum was going to be close either way, and whoever lost was going to have to accept the result. The UK Parliament are honour bound to accept the result, and the people who lost also need to realise this is a Democratic decision, and whatever the margin which was almost 4% they have to accept it, Im guessing its mainly a London based rebellion.
I dread to think what the repercussions would be, should either a 2nd Referendum be allowed, or Parliament votes against accepting the result.