I had recently come a cross the same issue with no heating also stop start was not working.
So the main pump solenoid connecter was loose re clipped it on and it made no difference so I punched a new aux pump located in the bumper access under passenger's wheel arch from euro part there was an option of the pierburg or a cheaper airtex.
For the purpase of elimination. I purchased the cheeper on which was smaller so I used heat resistant pluming foam for packing, the wiring clip and the pipe locations where in the same place so a good match and reatached with the same bracket.
The results where not instantly noticeable but after around 50 miles worked better stop start started working agane and after around 200 miles is working normally.
Hope this helps other just to note it had already been to a garage and there hanted to have it for 5 days removing the dash and heating system.
