If you pop the plug back in and fill the basin up, can you hear water draining from the basin? If you then put your hand around the top of the of the waste underside of the basin can you feel for a leak? Any puddling around the floor area beneath the waste?
Also try wrapping some cling film around the plug and see if that seals the waste.
If this is a council let property, really it should be them dealing with this!
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