UK Car Repair Questions? Ask a Mechanic for Answers ASAP
I have had many oil cooler failures for your concern.
I would replace your cooler, flush the cooling system, replace all the hoses, and the header tank etc.
Run just water for a week or so, then another flush out, then new coolant.
Engine oil and filter change, when happy with cooling system.
Hope this helps.
I hope my advice has been of assistance to you.