Locals waving Union flags gathered on the quayside to watch the British warships come in.
Andrea Jones, 46, works for an online gaming company and has lived in Gibraltar for 12 years.
She said the frigate's arrival was "a two-fingered salute towards Spain".
"I think the Gibraltarians are tending to be a bit more passionate at this moment in time," she said.
Retired Royal Gibraltar Police officer Michael Sanchez, 53, said he would like to see the British vessels off Gibraltar more often.
"It is getting to be out of control, it is not a spat any more," he said.
"It's a normal deployment but we need bigger assets to show them."
Tensions between Britain and Spain over Gibraltar's dropping of concrete blocks to the sea floor creating a reef have escalated during the last fortnight.
Spain says it was done to disrupt their fishing fleet.
Today's expected arrival of HMS Westminster, a type 23 frigate, is not part of the UK's response to the growing row.
The vessel left Portsmouth naval base in Hampshire six days ago to join nine other vessels taking part in a pre-planned international training exercise in the Mediterranean and Gulf.
Called operation Cougar '13, it is a long-planned deployment involving four Royal Navy warships, the lead commando group from 3 Commando Brigade Royal Marines and elements of naval air squadrons.
The type 23 frigate HMS Westminster will dock in Gibraltar as part of the exercise, while other ships in the task group expected to visit Spanish ports.
The vessels, which include helicopter carrier HMS Illustrious, will be taking part in what defence officials stressed was a long-scheduled deployment codenamed Cougar '13 in the Mediterranean and the Gulf.
The vessels set sail from Portsmouth as a diplomatic spat continued between the UK and Spain, triggered by the creation of an artificial reef by the Gibraltarian authorities which the Spanish claim will destroy fishing in the area.
Spanish defence minister, Pedro Morenes, has meanwhile said that it is "totally normal" for British warships to dock in Gibraltar in what is a "routine visit", according to reports.
Mr Morenes reportedly told the Europa Press news agency: "Neither the British nor the Spanish government have an interest in there being bad relations."
He also said that aircraft carrier HMS Illustrious had requested and been granted permission to stop off at the southern Spanish naval base of Rota on August 18, proving that there was no military escalation between the two countries