yep its oil pump fairly common on car with long service times in the past and ie ever run low on oil common,
link below for lci later type ie ecu controlled
below link for early non lci non ecu controlled.
link below for lci later type ie ecu controlled

Genuine Engine Oil Pump for Mini R55 R56 R57 LCI R58 R59 R60 R61 1.6 N16 & N18 | eBay
Genuine Mini Engine Oil Pump suitable for the following: Mini R55 Clubman - One, Cooper, Cooper S & JCW models (N16 & N18 engines only) Mini R56 Hatchback - One, Cooper, Cooper S & JCW models (N16 & N18 engines only) Mini R57 Convertible - One, Cooper, Cooper S & JCW models (N16 & N18 engines...
www.ebay.co.uk

Genuine Engine Oil Pump for Mini R55 R56 R57 R58 R59 One, Cooper, Cooper S & JCW | eBay
Find many great new & used options and get the best deals for Genuine Engine Oil Pump for Mini R55 R56 R57 R58 R59 One, Cooper, Cooper S & JCW at the best online prices at eBay! Free delivery for many products.
www.ebay.co.uk