What tankers ? they only had too few KC-130s which were already overstretched refueling Skyhawks and S.E.
The Mirage III were not capable of aerial refueling, can't remember if the Israeli types had that capability.
Another problem with the Mirage III fleet: too short range, and they run into a conundrum.
- they could be supersonic only at high altitude and with the afterburner
- Yet, distance was such: they could make it to the Falklands only at high altitude with no afterburner.
- if they went low and / or used the afterburner / to go supersonic and outrun a SHAR: game over, they would not return to the mainland.
The Daggers had slightly better range (the Israelis had improved that, first step from their IIIC toward the final Kfir) - but they were used only for attack.
I think the reason they retired the Mirage III fleet was that
- not aerial refuelable
- can't use their A.B, range too short
- can't go at low altitude, range too short
- can't use their supersonic dash capability against SHAR's to outrun them, range too short.
That made them simply useless for the air war over the Falklands - better to use the Daggers and Skyhawks that could at least make the trip with some bombs.
Also on the first day of the war the Mirage III pilots (painfully aware of the above mentioned limits) came at high altitude; and waited for the SHARs there. They hoped to used their supersonic dash capability or afterburner to dominate a high altitude fight, one way or another.
The Britishs however were no fools, and simply refused such fight - they stuck BARCAP-ing at low altitude.
Their reasoning
- After all those high altitude Mirages were no threat to the fleet
- And sooner rather than later (considering their range problem !) they would have to go down
a ) either to bomb the ships
b) or pick a fight with the SHARs
- Yet the SHARs could afford to wait, because Invincible and Hermes decks nearby
- the Mirages had no such luxury: mainland or die.
And the British logic paid.
The Mirages reluctantly went low to pick a fight, and there the SHARs kicked their asses, as everybody was subsonic there: plus AIM-9L and agility dominated old deltas with AIM-9Bs and not-much-better Magic-1s (Magic 2 might have been a different story but even for the French it was still in the future by some years).
After that the Mirages were found useless and retired (just like the antiquated Canberra bombers).
The reasoning: what mattered most was not killing SHARs but bombing the heck out of the RN invasion fleet; and there, Daggers and Skyhawks were far more useful in that role.
And since the southern airfields were so limited in capabilities... the useless Mirages had to go away.