2009 Freelander 2 . Blower works on cold but stops on hot. Fuse is ok.

Do you mean when the Air Conditioning is running automatically, or when you manually turn heater up and down.
Try manually turning it up and down, selecting different air vents, turning A/C on and off.

This should give us a better clue of what is working. FL2 XS SD4 Auto 2010 2012-2017 (21k - 91k miles) (MY2011)
FL2 Metropolis SD4 Auto 2014 2017- (16k - 77k+ miles) (MY2015)
Metro in its 11th Year of (Extended) LR Warranty / Full LR Service History
(Expensive, but Trouble/Worry free - hopefully?)

Check out the blower motor control module

You can run a diagnostic on the climate system with the proper software through OBDII.

Thanks for your replies.
My problem is with the hot/cold blower
Just tried different combinations :-
When both dials are on cold it’s ok
When passenger side dial is on hot it’s ok
When driver side dial is on hot the blower stops on both sides

Does the fan stop or is it that there is no airflow even though the fan is running which would indicate a problem with the flaps that direct airflow through the heater matrix?

Without having the codes read you are working blind.

It may be the ATC module if you want to throw some money at it replace the module with one from a scrappy be sure to match up the module codes, they are on a sticker at the back of the module

Link to Handbook-----
https://www.axelzone.ro/car/lr/fl2_handbook_2007.pdf

I take it that you have the 'Automatic Climate Control'.

If you look at the handbook there are a multitude of Buttons and Knobs to control output in either Manual or Auto modes.

Which functions work, --- in particular can you manually control the Fan Speed.

Which functions fail, ---- for example does the Defrost Program Button work.

It may help further if you say exactly which model and year you have. (You can fill in the details in your Member Profile) FL2 XS SD4 Auto 2010 2012-2017 (21k - 91k miles) (MY2011)
FL2 Metropolis SD4 Auto 2014 2017- (16k - 77k+ miles) (MY2015)
Metro in its 11th Year of (Extended) LR Warranty / Full LR Service History
(Expensive, but Trouble/Worry free - hopefully?)