I have just fitted new cork side cover gaskets and did them up quite tight but it now looks like they are leaking. A mate told me that they can leak if over-tightened, is this correct?

Hi,
That is correct. If you do make it too tight, gasket moves and starts leaking.
do just a finger tight and bit more. No pressure there so no need to make it tight.

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Oops

I have already over-tightened them, do I need to buy new seals?

Yes. See if you can find the red 'rubber' ones. They are about, but not many places stock them.

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Are you sure they are not leaking from around the bolt? Early ones have a red fibre washer there, the later (dished in) covers have a square section rubber ring inside a special retainer washer instead.

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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.