I have a 73 clubman with a sporadic speedo. When i first had the car 9mths ago speedo didnt work at all. Over the last few months it has started working, generally when the engine is cold, and for the first 3-5km, then stops. Suggests that heat is playing a part and something is slipping once warm.

I’ve checked the cable and it’s fine. Taken cable off the gearbox and confirmed that the cable to speedo works ok, spinning cable definitely drives the speedo. So i pretty sure it is the gearbox side.

I thought the speedo drive gears may be stripped, but that would be an all or nothing. Can’t figure out how it works sometimes. Is it possible that the nylon gear is slipping on the spindle ?

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1966 Mini Deluxe - “Gabby” 34 years under restoration and counting...
1970 MGBGT
1959 MGA

Does the odometer stop working when the speedo stops?
I have not seen a stripped gear, so I doubt it is that.
One more common problem I have seen is where the cable goes into the gearbox. The small square that the inner cable fits into wears and becomes "round", thus interrupting the drive. Try the inner cable in here and move it in and out to see if it slips at some point.
Bit tricky to do with the engine in the car, but that is a Mini

Also check the square on the bottom end of the cable, they wear too.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.