I doubt it. While the Midways lasted that long, they could be withdrawn for proper refits due to the availability of other carriers to fill the gap. Eagle would have been the sole large carrier in British service and so would have been worked hard with prolonged periods of time between refits. I could see the Falklands war (if it happened) being the being the straw that broke the camels back, and it being found when she returned that she was too worn out to repair.
They would have been used heavily, you're right, but with a commitment (based I'm sure on some kind of demand from the US for the presence of British as well as French fleet carriers to make up numbers due to post-Vietnam reductions, to which the reply from HMG's political/upper administrative class would've been "mumble mumble mumble top table and all that, chaps" and then getting on with it for as little money as they could get away with) to keep the carriers running post-Sixties, a U-turn on policy since the replacement plan (F-111K plus either Anglo-French VGFA or Panavia Tornado) had collapsed already,
Eagle especially could've held out longer, and with some proper patching
Ark could've made it through the Falklands and run on fumes into the middle of the decade. I suspect based on the survival rates of
Hermes/Vikrant and
Minas Gerais, and how relatively well
Bulwark was doing at the end, that
Eagle with her proper fix-up (just as
@Riain detailed) and
Ark with more work would've run on into the Eighties,
Ark to the middle of the decade and
Eagle up to the edge of the Nineties. At that point, of course, you have to look at replacements, but so are the French, and now you can have an Anglo-French replacement project with both nations looking at two ships apiece (or at the very least as the Cold War dies down one apiece trading off whose carrier is at sea.) That might have worked out as the best of both worlds compared to
Charles de Gaulle: British design teams might've come up with something less of a "let's try to leap forward further than we're capable" hot mess than
Charles de Gaulle, while the French, wanting to do the job and be done (much as, with the SEPECAT Jaguar, they exercised their veto and fixed the design just before the MoD teams tried to make three or four different aircraft out of it instead of building the damn thing) would veto the typical British procurement process -- a result of the fact that MoD
rotates its project-management personnel, which means (1) each management/design team try to put their own stamp on and you get multiple redesigns and (2) the longer a project runs the more jobs for the boys -- and say "you've drafted a nice ship. Now go build it.
On y va." That would've been a good outcome. Or if it's not a CdeG approximation, maybe it's a vehicle to have joint Anglo-French production of P.1216, and you get something like
Cavour only not trying to be an LPH at the same time so it has a proper hangar that really holds 30-35 aircraft, with c. 20-24 P.1216 and the rest AEW and helicopters for ASW, ship's flight, etc. Which is not the same capability as
Ark or
Clemenceau, but still nothing to sneeze at if you've got a good iteration of P.1216.