Hmmm...
I binned a flight last week because of failure of both AI and DI; but then it was a navex with a SRA at the other end, and it seemed a bit unfair to spring a no-gyro SRA on the poor Gloucester controller who has only primary radar to begin with.
Like you I was made to fly a couple of circuits with no instruments (did you learn at Welshpool as well?!) to show it could be done.
I think I could divide into 2 cases:
Failure of any of these in flight would cause me to divert immediately to the nearest airfield and probably declare a PAN:
altimeter
ASI
compass
Failure of any of the following before flight would cause me to cancel the (VFR) flight:
any of the above plus
VSI
turn & slip
balance ball(?)
VHF radio (yes, I know lots of you don't use radio, but you don't fly from Kidlington...)
In other words, if I lost, say, the turn & slip in flight, I'd carry on to my destination or go back home, but I wouldn't divert to the nearest airfield.
And, if the weather was marginal, I wouldn't take off without:
ADF
as that's the only way back into Kidlington in IMC (otherwise it's a SRA/PAR into a nearby military airfield and talk my way out of it!)
Tim