More test equipment required :-(
Many IR testers already show you the voltage they have achieved during the test. For a good circuit giving many Mohm then it is usually a bit above the 250/500/1000V that you have set your meter to, but if you have a soggy circuit then it might well be down in the tens or hundred or so volts.
If you test a varistor (MOV) style of SPD then it starts conducting at a bit above the usual peak AC voltage. So with the max UK being 253V RMS that is 253 * sqrt(2) = 358V peak and you don't want the SPD toasting on normal sort of volts so they might be designed to
start conduction (~1mA) in the 400-500V region, and are conducting heavily (in the 10kA region) at the 1-1.5kV sort of point.
Gas discharge tubes (GDT) are a bit different, they show nothing typically until near peak volts (often 1kV-ish) then flash in to conduction down to ~100V as they dissipate the energy, but usually they are kept for Type 1 SPD, or sometimes the N-E protection side of a dual MOV L-N and GDT N-E device.
Deploying GDT on L-N is trickier as you don't want follow-through where the normal AC power keeps the thing burning, so some units have a low-breakdown MOV and GDT in series, etc. But N-E side has little normal AC volts so no follow-through arcing problem.
Anyway, back to testing - if you run a IR test on a SPD and watch the volts you will see it limit in the 400-500V sort of region, that is why they show tens of Meg if tested at 250V but usually well under 1M if tested at 500V. Attempting to test at 1kV would prove it (clamping to ~500V-ish) but if the SPD is missing/broken/not connected OK you need to be sure the rest of the installation is safe to test at 1kV which is not really the case for a nominal 230V system.
The SPD will be fine, so lifting its cable to test it at 1kV will show it working (or not) but usually you don't want to modify a system during testing if at all possible. Here the cheaper SPD that require a MCB for the L supply have a bit of an advantage!