Morris Minor Owners Club

I dont appear to have much luck on the reliability of by 1098 engine. I had one rebuilt from a block and parts from my worn out but recently rebuilt engine. The middle core plug has blown out again. So probably another head gasget is needed as well.

Any idea what could cause the pressurising of the cooling system (apart from the head gasget failing)?

More importantly, are there any companies that sell replacement engines?

Why do you think the head gasket has failed? Core plugs do blow out sometimes - its happened to me and no harm done. Blowing out a second time makes me wonder if the replacement fitted properly first time? Hard to tell at a distance.
Google 'Morris Minor replacement engine' and stuff will come up. Shouldn't be a problem to find what you want.

The core plug has to be well hammered in the centre to flatten and so grip the sides of the hole in the block. If the core plug is not secured properly it will be blown out even with a 7lb radiator cap. Even worse with a 15lb cap. Make sure that the seat for the core plug in the block is spotlessly clean and free from crud before fitting the core plug.

I don't see why a head gasket is relevant to a core plug blowing out.
Sorry to tell you this, but 'poor workman blaming their tools' etc.
If a core plug is correctly fitted, the radiator cap is going to let steam out long before the core plug even starts to leak, let alone 'blow out'...
A domed core plug, beaten flat with a suitable drift, is going take somewhere in the region of 50-100psi before that amount of interference fit is overcome.
Your Radiator Cap is probably only 4psi.
The radiator cap is only there to raise the boiling point of the coolant.
A 4psi cap raises the boiling point by about 12degF, so pure water would boil at about 224degF instead of 212degF.
IMHO, there's no way a correctly fitted Core Plug will blow out before the radiator system is letting steam and hot water out.