An air gap between insulation and roof deck won't be of any use unless it's vented to the outside.
If you put insulation up as stated above, you will need ventilation between each rafter, which really should be cross ventilation, a vent at each end.
I don't now how handy you are, but the longer term fix here would be to strip the roof covering, raise up the front of the roof so that it's more flat than it is now. Infill between the top of the windows and the joists, maybe a very short stud wall.
Then a stick down vapour barrier on top of the roof deck, insulate on top of the deck, new roof covering (felt/rubber/fibreglass) and flashing. It will probably need the joist depth upgrading too, although you'd probably get away with glueing and screwing 2x2 to the underside of the existing joists.
As it is, you'll probably see the roof deck starting to rot within about 5 years.
If 5 years is long enough to save up for a new extension then crack on.