After still having problems starting from cold despite the fitting of an alternator, the old boy went back to the mechanic. I had the luxury(?) of an early model Mundaneo on loan from said garage while the chief looked over the moggy, and while it was lovely to listen to Wogan on the way to work every morning, I was grateful for the return of my beloved Minor this morning. Turns out that the distributor and various other parts were, I think, soiled and messy and not connecting correctly. I think. Sadly, all went a bit wrong and a cylinder stopped working halfway home, so I turned around and headed back, thankfully finding that the mechanic hadn't shut up shop for the afternoon and was still available.
It appears that my car has an ongoing slight health problem.

Apparently it's very difficult to trace the exact source of an oil leak, and it also might require maching and therefor the cost of fixing what is allegedly a common problem would be prohibitive. I've also been told that the engine )original one still in there) is tired, due in no small part to the niggardly maintenance habits of previous owners.
I guess what I'm thinking of is putting a new/reconditioned engine in eventually - would this solve the oil leak problem? Also, would I need new brakes/other requirements to keep up with a new engine? Plus, would a non-Minor, but still Morris-made, engine, be suitable? I have a bit of a thing about wanting to keep as much of the car Morris-made as possible, and although the thought of a beefed-up engine is nice, I'd like to keep it all Morris brand.
And is a new engine really necessary? My mechanic doesn't think so and I trust him, but I hate to see my car smoking from the rear and I'm worried that it will just get even more worn out and tired. And is this a common problem, as my mechanic says he knows of a couple of other owners with the same issue?