Yes there were and they largely did nothing as they were not allowed to enter the war, so they stayed in their bases. When Turkey completed its invasion the Brits were prepared to try and prevent it by the US 'vetoed' that option. They are also part of the UN forces monitoring the border as well as having bases there.

The situation makes more sense with a bit of historical context.

Cyprus was under British administration and during the 1950's British troops were fighting a reasonably bloody insurgency against a group known as EOKA, who's main aim was unification of Cyprus with Greece. Following the resolution to this conflict Cyprus was given independence, however, on the condition that there was to be in unification with Greece. Also, due to its strategic positioning in the Eastern Mediterranean the British kept two chunks of the South of the island, which to this day remain Sovereign British territory.

Fast forward to 1974 and Turkey decides to launch an invasion onto the North of the island. Since at this point Cyprus is an independent nation and the British Territories are on the South of the island British troops remain put on the basis that the Turkish have not incurred within British borders. Hostilities end with no direct British military involvement and an armistice that splits the island roughly in half.

Today there is still a significant British military presence in what are known as the two Sovereign Base Areas. In addition there is a separate UN peacekeeping force, to which the British provide a contribution to, sat on the border between the two Cyprus's.

Interesting sidenote, even 40 years later there is a lot of eccentricity and hostility between the North and South. If you travel to the North and allow the border guards to stamp your passport, the South won't let you back in. There are also frequent displays of 'oneupmanship' along the border, such as residents on both sides constructing extensions to flagpoles to raise their countries flag higher. To top it off a 500m wide Northern Cyprus flag is whitewashed into the hills overlooking the capital, Nicosia.

TL;DR The Turkish invasion never threatened British territory, so British troops remained neutral during the conflict.