Morris Minor Owners Club

That does sound pretty rough.
The rocker arms can wear through the hardening where they meet the valves making them very hard to adjust properly.
The rocker shaft can end up looking more like a crank shaft too with poor lubrication.

Sounds like a Talbot engine circa. 1980...

This is actually much louder than it should be. You sure they are adjusted properly?

If you are sure it is coming from the back of the engine, then the possible causes are:-

1.Worn rocker shaft - easily checked by removing rocker gear. Replacement about £5
2. Worn rocker arm - same as above.
3. No.7 or 8 Cam follower. remove tappet chest cover, fish out and check.
4. No. 4 Piston - ring(s), if you have good compression it is unlikely, but possible, can be checked by head removal, and if
necessary piston removal by releasing big ends via sump (engine still in car). Big end can be checked also.
5. The only other moving part in the back of the engine is the oil pump, which runs off the back of the camshaft. Engine
removal is required for this.

As you can see from the above, start with the simple things, and eliminate them one at a time, keeping the cost and work down.

Is the rubber grommet still in place on the top of the bellhousing? Could something have dropped into the bell housing and is rattling around.

It WILL rattle on as it is for a long time to come...