Could be either really.
If only on startup and it goes away, except at bottom of hills- think valve stem seals.
If it does it under load, it's the rings...
I don't believe in re-ringing Minis- if they are worn out and pumping oil, the bore is worn oval/tapered too. There is so much work stripping and reassembling it, I think it's false economy not to bore & hone it, and fit the next size up pistons and rings.
Good oversize pistons are cheap as chips these days. And a 4 cylinder rebore & hone is $100-$150.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.
