So is it possible that you ask for vectors to the ILS but are given "cleared to approach" instead? - implying that you fly the procedure instead - or would the instruction be more explicit?
This could happen only outside the UK, but no, if you are being vectored you would not fly the published procedure. You would intercept the localiser when you get to it.
If ATC English is suspect (true much of the time in southern Europe) it is best to help them out by e.g. reporting "localiser established". In Spain, if ATC did not understand something you said they ignore the call (presumably as it leaves no evidence against the ATCO on the tape) and they ignore the call even if you repeat it.
Remember that in all flight, the vertical and horizontal clearances are separate. So, cleared for such and such SID is the lateral clearance, cleared to climb FL090 is the vertical clearance. Unless otherwise specified on the plate
But when you are "cleared for the approach" the two clearances merge; you can descend to the platform and fly the approach as published, vertically and laterally. In the UK, the phrase is used only for non-ILS approaches.
What has confused me, in Greece mainly I think, is being told "report ready to commence the approach". What exactly is that?
Intercepting the GP from above is the norm at larger airports
Sure but only from just above the GS, where the GS indication is not right off the scale

If you get vectored so the GS is off scale, you
must go missed.
BTW Roffa a TB20 can fly the ILS at almost the same speeds as a 737. Once, in Prague, the GS was 210kt (descent + tailwind) and ATC told me to slow down. I do have to slow down a bit more at the end though

In the UK, most big-airport ATC is not used to mixing light singles with big jets because of the £500 landing fee.