That's correct, turn the key to start and it doesn't crank at all.
I've now checked the connector - it's fine, totally clean inside - I've measured the voltage at the starter solenoid: it goes down to about 8.8V while cranking, and voltage at the battery itself is about 9.5 while cranking, so there is a bit of drop between the battery and the solenoid. I haven't been able to take the measurements while it's having the issue though as it's cranking fine at the moment, when it's having trouble again I will try to measure to see if there's a difference somewhere.
I've swapped the starter relay with the one on the end (the heater rear window one) and we'll see if it trouble again in the future.