If it's loose in the outer column it's the upper bush worn.
If it moves up and down ie. in & out, could be the pinch bolt loose, or the slot has closed up. If so take it off and stick a hacksaw thru it again. There must be a gap there when the bolt has been tightened, or the spline inside will wear and strip.
A friend of mine put his Mini up a kerb and thru someone's garden last week because of this. DON'T take chances..!
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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.