1st rule of British cars: If its not leaking or useing oil then there is something wrong with it.
If its losing oil out of the new breather cap then you will be able to see it, literaly flowing over the rocker cover.
First you need to work out where its losing the oil from, being old and MG it could be anywhere, but get in as close and personal as you can with the engine and try and find the source.
There are three main possiblities:
1, most likly considering the cars age; Its simply burning it, as the valve guides and pistons bores wear it allows the oil to enter the compustion chamber where its burned off. You will see it as a blue smoke in the exhaust. Of course you can rule this out of the engine has been recently rebuilt, but if its oringal then you could lose as much as 1/4 of a liter every fill up.
2. An oil leak somewhere. Most likely a gasket that is old and worn out. You should be able to see where the oil is flowing over the engine.
I would start with your new rocker cover, the cork gaskets used compress over time, and you might simply need to tighten it down a little more.
Also check time cover on the frount, the sump, and around the mechanical fuel pump. Once you find it you simply need to replace the relevant gasket, which is an easy afternoon job on all but the sump.
Its also possible, infact given the age of the engine quite likly that the frount or back main seals will be worn and also leaking. There is little you can do to fix with out spending a lot of money, and your better off leaving them for a complete engine rebuild.
A leaking rear main will show as oil dripping out of the bellhousing.
You could be losing as much .5L every tank of gas.
3. A combination of the above 2, which considering how much your losing is the most likely.
If the new breather cap is unable to relieve the pressure in the system to the same extent the orginal did then it would most deffinitly increase the rate of oil loss from any of the above, but the only real way to tell would be to refit your old rocker cover, and since your removed all the emissions garbage simply run the vent pipe into a small plastic bottle (600ml coke bottle is perfect).
And of course the best advice I can give is to find and join the nearest branck of the MG club. Its one of the worlds largest car clubs, and by far and away the best source of information and parts.