Let's remember that Kate isn't conversant with all the technicalities of part/tool names, fellas.
If it's the oil cooler, Kate, this is like a small radiator, sitting in the bowels of the engine unfortunately, (where Broocie was at Shifnal), through which the oil passes to be maintained at a safe temperature by water from the cooling system. The oil cooler itself will be intact, otherwise you would have noticed Loo Knee's gungy mess in your cooling system expansion tank. The water flow is obviously run through pipes to the oil cooler and it seems there was evidence of the sealing having been botched, and it does seem that this has broken down causing your present problem.
The solution would be to strip the engine to the same point as at Shifnal, and then go a bit further to reseal the oil cooler plate with the correct equipment or, as Loo Knee suggests, replace the oil cooler as well, if necessary, as a belt and braces job.
If you could find someone to help and/or advise and provide the few extra tools required, you could do it yourself perfectly well, but it is going to cost you money for parts and you would be wise to allow for the car being off the road for a while so that you could take your time.
It's a pity you don't have a garage you can trust. It might be an option to offer to pay a member with the appropriate knowledge to do the work for/with you.