Checking radiator cooling fan

To test the fan's operation directly, on cars with the lucasfob (square) without AC.
Remove the yellow relay under the bonnet and use a suitable wire shunt to bridge these two points. With the ignition on, the fan should run!
 

Does that apply to both f & tf David? It’s such a long time since I had the tf I can’t remember now.
Information like this is useful to store in a dusty drawer of my brain, instead of relying on someone else’s dusty drawer.
Thanks.
M

It does apply to MG F and mk1 MG TF (Lucas type fob) but only in case you do not have aircon fitted. It does not apply to mk2 MG TF (Pektron fob type).

Thanks Roverlike, I was searching high & low for the yellow relay.........mine has AC!

All Oz spec cars have AC, which is why I made the suggestions I did.

Roverlike wrote:

It does apply to MG F and mk1 MG TF (Lucas type fob) but only in case you do not have aircon fitted. It does not apply to mk2 MG TF (Pektron fob type).

David Aiketgate replied:-
Thanks Damir,
I will amend my post to reflect that...
David

 

OK. Thanks for the guidance, process of elimination indicates the ECM isn't activating the fan which otherwise does run.
I think I heard somewhere that there are exchange services offered by some firms - is this correct and if so, where to go? Anywhere here in Oz (Cobber?)
It's a Mk1 TF with square fob, Lucas.

Not in Oz that I'm aware of.
I wouldn't think it too difficult for an electronics geek to fix.
On my Triumph TR7 it had a little box of tricks made by Pektron, what it did was control the pop up headlights with a delay timer so the lights would momentarily stay up so as the lights could be flashed. It had shat itself so I got a geek mate to crack it open and he replaced all the crap soldered to the circuit board but the chip.....Sorted!
I ended up not using it anyway as I ended up discreetly fitting the car with both fog and driving lights, under the front bumper, it made more sense to use the driving lights for flashing purposes (saves the pop up mechanism for unnecessary ware and tear)

 

If in doubt you could always create your own fan control circuit using one of theses and a simple relay. in line temp switch

I'm still chasing this overheating issue so further suggestions will be appreciated.
Reminder: MG TF 2002 135 with air. Getting near max temp (almost to the 4/4 point) in stop-start traffic, returns to normal temp quickly when moving. The engine bay fan activates when the car is hot therefor temperature sensor seems to be working.
So, as suggested, the engine fan has been checked and found to work fine when hit with 12 volts, so can now assume it is not getting a signal to turn on as coolant level rises. 
I've now found that the AC isn't working although the refrigerant level is fine and the AC guy suggests it is unlikely that the compressor is faulty, thus suspects it's not getting the appropriate signal to turn on. (The idea was to turn on the air to activate the AC fan thus cooling the radiator, at least until a solution to possible ECU fault can be found.)
Also, I have learnt that the relay sitting between the fuse box and the 70 amp fuse under the front bonnet operates the cooling fans. My question now is, does this relay also operate the AC switching? If so, could it be the relay at fault and not the ECU? Guess I'm looking/hoping for a cause other than the ECU - I've been in communication with Bitz and they don't have the appropriate ECU set as the air-conditioned models there in the UK are rare.

One relay operates only one fan. However since you have AC, at place you mentioned you do not have one yellow relay but black box of 4 relays pack together as you can see in this thread:  https://www.the-t-bar.com/forum/roverlike-s-guides/97846-mg-f-tf-fuse-relay-listing  part number YWB100801. In that box you have both relays which operates cooling fan and AC fan.

Brilliant, thanks Roverlike. 
The info you provided includes Additional Relays and the relay I was wondering about is an 'Air Conditioning Pack Relay Module" which controls the radiator fans + the AC compressor clutch, the items which have failed. 
I imagine the relay will be easier to find either new or second hand and will certainly be easier to fit and less worrisome than the ECU sets.
I'm very grateful.