The car park, between the golf course and beach by the boat houses, has been closed since March due to the coronavirus pandemic.
It is operated by the village burgage holders and talks have been held with the parish council on what steps to take now that lockdown restrictions have been eased.
Coun Shaun Whyte, parish council chairman, said: “The burgage holders are very keen that we provide a united view as to when the car park should open. I would absolutely welcome that cooperation with the parish council in coming to a decision.
“We need to try and determine an outcome which is in the best interests of the village.
“It’s slightly awkward for them in that they don’t have payment machines, they would have to have a lady at the entrance taking money. It’s not a cashless transaction so it would be awkward for her in terms of shielding.”
Coun Mac McHugh pointed out that the car park would have to be resurfaced before it reopens.
“It’s in no state to reopen at the moment with all the rocks,” he said.
Coun Gordon Castle, county councillor, said: “It’s a dilemma. There has been an easing of government restrictions in terms of allowing people to drive where they like for exercise.
“That means it is highly likely people will want to go to the coast in decent weather. The trouble is that if we don’t open the car parks there will be enormous pressure on existing spaces for residents. If we do open the car parks it’s tantamount to encouraging people to come to coastal resorts. That’s the difficult decision that has to be made.
“My understanding is that the burgage holders usually take their lead from the county council but that, of course, is not obligatory.”
When the car park was closed, the county council provided a sign at the top of the road down to the beach and a ‘stay away to save lives’ sign at the village entrance.