David Cameron told Spanish prime minister Mariano Rajoy the situation at the border with Gibraltar is "not acceptable" as the two leaders held talks aimed at calming tensions.

Downing Street said that in the phone call Mr Rajoy agreed to reducing measures at the border that have led to lengthy delays for Gibraltarians, but a statement issued by the Spanish government made no reference to any such concession and insisted procedures were proportionate.

Speaking after the call, the Prime Minister said he was very clear Britain "will always stand up for the people of Gibraltar".

His intervention followed a formal protest by Britain's ambassador in Madrid over "disproportionate" checks at the border and Spanish threats to levy a charge on vehicles crossing the border and to close airspace.

The dispute has flared up over claims Gibraltarian authorities damaged fishing grounds after the creation of an artificial reef.

Mr Cameron said: "I had a clear and constructive conversation with the Spanish prime minister.

"I think it is important that we recognise it is not acceptable, what has been happening with the people of Gibraltar, in terms of delays and other things that they have faced.

"I made that point clear. Of course, there is a fishing dispute between Gibraltar and Spain and that needs to be settled and we agreed that should be settled, but it is not right to escalate things in the way that has been done and I made that very clear to the Spanish prime minister."

Mr Cameron added that he was pleased the leaders had agreed to start resolving the issue.

Speaking on a visit to the North Devon Show, he said: "I am satisfied that we agreed to make some progress but I will only really be satisfied when this is properly de-escalated and the interests of people in Gibraltar are properly looked after."

A No 10 spokeswoman said the Prime Minister had stressed the situation posed a real threat to the UK-Spanish relationship.

"The PM made clear that our position on the sovereignty of Gibraltar and its surrounding waters will not change. He also reiterated, as the PM and Mr Rajoy had previously agreed, that the issue should not damage our bilateral relations," she said.

However, a statement issued by the government in Madrid defended the border controls, claiming they were necessary to prevent smuggling. "The head of the Spanish Government reiterated his will to find as soon as is possible a solution to the current situation created by the Gibraltar authorities, which has produced a deep unease and a great concern because it hurts the environment and fishing activity," it said.

"In this respect, President Rajoy argued to Prime Minister Cameron that the unilateral act of installing the blocks of cement in the bay of Algeciras was unacceptable."