Labour’s pledge to hold a second referendum would be political suicide and harm its chances of winning seats in the county at an election.
Brendan Chilton, an Ashford councillor and general secretary of the Labour Leave campaign, warned the party faced an uphill battle in key target seats if it endorsed a second vote.
In a stark message, he said: “It would present us with enormous political challenges in Kent.
"If you look at all the seats that Labour has ever held in the county, they all voted overwhelmingly to leave.
"If you look at the make-up, they are all predominantly working class.
"It would be extremely difficult for us. If you look at the seats that Ukip gained in councils when they were at their, they were mostly marginal Labour ones.
"This would not help Labour in Kent. In fact it would have a detrimental affect both nationally and locally.
“If you look at the seats that we hold on Kent County Council, they are all marginal ones and have mostly leave constituents.
"I would like to see how our candidates would go about campaigning when the party is emphatically remain.”
"Supporting a referendum and remain would have a detrimental impact on our prospects in Kent" - Cllr Brendan Chilton
He said while Labour would benefit from having a decisive position on Brexit, its current policy was confused.
The councillor added: “For the last three years, let’s face it, half the membership haven’t known what our policy has been, so how can we expect the public to know?
“Supporting a referendum and remain would have a detrimental impact on our prospects in Kent.
"Frankly, our failure to pick a side has led to the position we are in.
"We came third in a national election and I dread to think where we were in Kent.
"This is not a position that a party that hopes to form the next government should be in.”
Canterbury MP Rosie Duffield, the county’s only Labour MP, has backed a second vote.
Labour leader Jeremy Corbyn has written a letter to MPs indicating the shift in policy after the party performed poorly in the EU election. It just held its one seat in the South East region.
He writes: “It is clear that the deadlock in parliament can now only be broken by the issue going back to the people through a general election or a public vote.
"We are ready to support a public vote on any deal.”
Meanwhile, a third Conservative Kent MP has announced he is backing Dominic Raab for the leader’s job.