The Foreign Office lodged a formal complaint with Spain after a British diplomatic bag was opened by a Spanish border guard.
Gibraltar's chief minister is to meet David Cameron amid allegations that Spanish border police have come under attack from angry motorists.
Pictures posted on Twitter show Spanish divers hanging flags over the controversial boulders.
The European Commission has urged UK and Spanish authorities to work together and "strengthen dialogue" at the Gibraltar border.
An EU Commission statement suggested "daily cooperation between the authorities working on each side of the border" to help combat tobacco smuggling.
Commuters faced delays of several hours over the summer caused by stringent checks imposed by the Spanish during a diplomatic row over an artificial reef sunk off Gibraltar.
The European Commission said Spain should "optimise" its profiling system at the Gibraltar border "in order to reduce the large amount of random border controls".
However, the EU said the Spanish authorities had not broken any EU laws with its tight border checks.
"The Commission has not found evidence to conclude that the checks on persons and goods as operated by the Spanish authorities at the crossing point ... have infringed the relevant provisions of Union law," it said in a statement.
The EU Commission has said it has found no evidence that checks by Spanish authorities at the Gibraltar border broke European law.
Sources here in Brussels are telling me they think the British and Spanish will be receiving a letter from the Commission, advising them on ways to improve the relationship at the border and to co-operate to reduce tensions.
The European Commission will make "key announcements" about the Gibraltar border issue within the next hour, a spokesperson said.
Olivier Bailly from the EU Commission said on Twitter that there would be "messages for both Spain and the UK" in a press conference at 1100 GMT:
A retired Royal Marine who led British forces in Afghanistan is set to take over as the new governor of Gibraltar, the Foreign Office said.
Lieutenant General Sir James Dutton will become the Queen's representative on the Rock from December when Vice-Admiral Sir Adrian Johns steps down after four years in the position
The appointment comes with the UK and Spain locked in a diplomatic spat over the Madrid government's imposition of border checks in a row with the Rock over fishing rights.
A planned cross-border protest ride by Spanish bikers will be blocked from entering Gibraltar, police said.
The "Marcha de Moteros" (March of Bikers) is being promoted on Facebook as a "citizens action" in support of Spanish fishermen and border police in the ongoing row with the UK and the British Overseas Territory.
A FB site 'Marcha de Moteros' in Gib in support of fishermen is making people anxious. Rest assured such demo will be stopped at frontier
T-shirts that proclaim Spain's sovereignty over Gibraltar, which was ceded to Britain 300 years ago, are being sold on eBay for bikers to wear on the day.
The Royal Gibraltar Police said it would stop any bikers who arrived at the frontier from crossing to avoid breaches of the peace.
After the talks, a Number 10 spokeswoman said:
The meeting reaffirmed the existing strong and historic bonds between the UK and Gibraltar and the Prime Minister repeated his commitment to stand shoulder to shoulder with the people of Gibraltar.
They discussed the unacceptable delays at the Spanish/Gibraltar border and agreed that these are damaging to the people and economies of Gibraltar and Spain.
They agreed that efforts should remain concentrated on finding a diplomatic solution, in line with the Foreign Secretary's proposals last year for ad hoc dialogue.
David Cameron has met Gibraltar's Chief Minister Fabian Picardo at Downing Street to discuss the UK's border dispute with Spain.
- Mr Picardo's visit to the UK saw him meet with Foreign Secretary William Hague on Wednesday, a meeting he said showed that the UK and Gibraltar governments "remain in lockstep" over the disagreement.
- The spat effects regular commuters as up to 8,000 Spaniards living mainly in the nearby towns of La Linea and Algeciras travel daily to Gibraltar for work.
- Yesterday, the Gibraltar government accused Spain of introducing an export ban on construction materials to punish the enclave.