Your water pump seal has probably failed too. There is a hole in the pump casing which drips when the seal fails. This then corrodes the oil pipes beneath. Great piece of design.
I think some people have managed to replace the pipes with a rubber type.
Following reports on here, I went off to a hydraulic hose outfit with old pipe as a pattern, who sorted me out for £25 or so. Threaded fittings either end plus rubber hose that they assured me was perfectly adequate and it has been. A bit of trouble fitting cos it was a bit short to bend easily through 90 degrees. If I was doing again would get an elbow fitting on one end.
I had this problem. I found one of the two oil pipes badly corroded, the other was OK. Purchased a new one and coated both in epoxy in the hope this will svae them the next time the seal goes.