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.