If it’s the water pump it’ll be throwing up error codes, [ref]Jeverson28[/ref], have you had the car scanned yet? If not suggest that as your starting point.
Thread here showing error codes expected if water pump
https://z4-forum.com/forum/viewtopic.php?t=133163
It’s been a while since I’ve had a HG replaced but £2k seems VERY expensive if it’s just a gasket change with no other repair imo