The man, who referenced his work as a Vote Leave coordinator during the campaign, attacked MPs from Labour and the Liberal Democrats for their attempts to try to secure a rerun of the June 23 vote.
He accused the parties of not backing Brexit because they were “worried about losing left-wing supporters”.
The Question Time audience member said calls for a second referendum were "democracy deniers"
I think this needs addressing – they’re democracy deniers
Question Time audience member
Although admitting to the audience he had voted to Remain, he said the outcome of the result must be respected.
“I voted Remain, cards on the table, so I’m not particular happy we are where we are, but we are where we are.
“And the whole point in democracy in a free society like ours is that when you go and vote, it really matters. It’s incredibly important how you vote in elections and referendums.
“And the point about the second referendum, this was the second referendum. We had the first one back in the mid-1970s, we voted to go into Europe. We’ve now had another one to leave Europe?”
The man claimed to have been a Vote Leave coordinator during the referendum
Backing up Mr Morgan, the Question Time audience member, said: “I was the Vote Leave coordinator for Peterborough [where Thursday night's show was held] and I never thought I’d say this but I completely agree with Piers.
“To say immigration was not the main contributing issue that people say they weren’t concerned about is ridiculous.
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“The fact that Labour, the Lib Dems are calling for second referendums or ignoring the fact of immigration is mainly because they’re worried about losing left-wing supporters and is just absolutely ridiculous.
“I think this needs addressing – they’re democracy deniers!"
Liberal Democrat Alistair Carmichael said there should be a referendum on the Brexit terms
Also among the panel for the BBC show was Liberal Democrat Alistair Carmichael, the former Scottish Secretary.
The MP for Orkney and Shetland repeated the party line, led by Tim Farron, for a second referendum on the final terms of Brexit.
He demanded Britons were given their say again “once we know what the shape of the deal is with the EU”.