If it's got sideways movement it's because the crappy Chinese made caps are too big diameter to fit the dizzy body properly.
I found a new Lucas 45D cap the loosest.
You may find the plug cable posts can hit the rotor. I had to machine .5mm off my new rotor so it cleared.
Bloody aftermarket parts...

[edit] if the metal clips are loose, you can remove and bend them shorter in a vice.
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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.
