If we’re going on the basis of kills scored; British made (but not necessarily flown by the RAF or Fleet Air Arm), and not the Sea Harrier, then the Hunter leads the way - the Indians, Iraqis and Jordanians scored victories with their aircraft. In fact, the Hunter probably outscores the Sea Harrier.
We can’t be sure of the exact numbers, given that overclaiming (genuine errors and propaganda) is a constant risk, but the Air Combat Information Group website suggests the following:
The Jordanian Hunters appear to have shot down two Israeli aircraft between 1964 and 1966, and inflicted damage on several more.
Iraqi Hunters appear to have destroyed up to eight Israeli aircraft between 1967 and 1973.
Indian Hunters would seem to have been responsible for the destruction of up to 23 Pakistani aircraft in 1965 and 1971. By the by, it would seem that the IAF Gnats/Ajeets might have scored up to 19 kills.
Again, I can’t be certain of these figures, but throw them in for interest.
As for the RAF, there are several mysterious ones…
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There are persistant rumours that an RAF Hunter FGA 9 brought down a MiG-17 during the ‘Confrontation’ with Indonesia, and even stronger suggestions that a Gloster Javelin shot down an Indonesian C-130 during the same conflict. Both - especially the latter - are said to have been manoeuvre kills, but a groundcrew member from 60 Sqn, RAF has reported that on the evening that the C-130 went down, a Javelin returned to base missing a Firestreak (IR missile). It was claimed that this was an emergency jettison rather than a firing, but the groundcrew noted that the firing lead which would have been severed during an emergency jettisoning of the weapon was still on the rail - and it wasn’t severed when the weapon was fired…
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Also, there are suggestions that a de Havilland Venom ran into a MiG-15 during the Suez affair and shot it down. I’ve not seen the evidence for this myself, but a couple of usually trustworthy sources are convinced that this happened (based on chatting to the pilots and drawing inferences from some of the remarks made), but was ‘hushed up’ for some reason.
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The C-130 vs Hunter FGA 9. In 1966, a C-130 was stolen by a US airman from RAF Mildenhall. It is very likely that he lost control of the aircraft and crashed into the sea, having been shadowed by RAF Lightnings and a French Mirage III. However, the rumour that a Hunter from (variously) RAF Brawdy, RAF Boscombe Down or RAF Chivenor was sent up with a full load of 30mm ammunition and came back with rather less has never been totally discredited…
As for the most active aircraft in terms of delivering weapons against enemy targets, that’s probably going to be the Canberra. Saw action in Malaya, at Suez, during the Indonesian confrontation, in Vietnam, during the Indo-Pakistani wars, in the Congo (by India on behalf of the UN), by the SAAF in Namiba and elsewhere, by the Rhodesian AF during the UDI wars, and by the Argentine AF during the Falklands/Malvinas war
The Hunter appears again as a rival - as well as the nations just mentioned in the bit about kills, the RAF used it in combat, as did the Lebanese, Rhodesian and Somalia air forces (and the Omani air force might have flown it in combat, but I’d have to check).
The Tornado doesn’t really count as a British aircraft as it’s a collaborative project, ditto the Jaguar and ditto the Harrier after the GR 3 model.