As it's a mk1** it should have the same cylinder retention as a mk 6.
On the left side there should be three screws - bottom most one with a large slot - unscrew it and move the lever it holds up - this is what holds the cylinder in place. Put the cylinder in, latch that lever - does it start working properly?
If not it will need to be disassembled further to see why things are not latching. Please mind the screw heads - too many get damaged. If you need to send it to a smith or need parts - PM, I have a partial donor mkVI.
(You may also get more answers in the antiques sub-forum)