I had a similar problem on a fairly low mileage Citroen, ( About 35,000 miles ) I was advised by the Dealer that it was a bad engine and they had heard about several garages with the same problem, So after warning the customer that it might not fix it, I did an oil flush and an oil and filter change with a genuine filter and it cured it.

It might not be the same as yours, but you have to try the easiest things first, I would have definitely changed the filter before thinking about the pump.