It may well be officially cheaper, on eBay though it was about £450 for the n14 and £799! For the n18. Mini themselves are just over £500 if I remember correctly.
I was given the details of a specialist in cardiff called Swiss something, I checked in their prices for the service and it actually worked out £5 cheaper for the mini dealer to do it. Not what I expected and I'm sure if I'd spoken to the specialist they'd have beaten the price, just didn't seem worth the hassle. Booked it in on Monday with Mini and they're having it tomorrow, called them about 10 mins ago on the off chance that they possibly could sort a courtesy car for me, they didn't have one available but booked an enterprise car for me. Admittedly the lady said it won't be a Mini or a BMW but who cares, it's only to get me home and back to collect it when it's ready.
Very impressed so far with mini Cardiff. My previous experience with them was that they were a little bit snooty and rather dismissive, that was a couple of years ago so they've obviously stepped up their game
Just fingers crossed now that the pump and a full service fixes the issue and it's all back to normal running