Sounds like it could be the connection on the fuel cut off solenoid. Thin wire with spade end could be just hanging on for dear life.
Where would I find this?
...if it's not turning over it will probably be the solenoid wire on the starter motor. Same, thin wire, spade end attached to starter motor.
Sounds very familiar. I had the very same symptoms on my Defender TD5 and it turned out to be a poor connection, corrected simply by wiggling the small, exciter wire to the starter solenoid (which I was shown by the RAC Man ...). Corrected in seconds.
Good luck!