Lighting plugged into a 13 amp socket is fine.
Connect the lights together with cable or flex, then add a piece of 3 core flex to the last light from the connector block and add a 13 amp plug top to other end. Reduce the size of the fuse in the plug top to 5 or 3 amp and simply plug it in.
Providing the socket you're plugging it into is "health" ie wired in correct sized cable, protected by correct method (ie correctly sized fuse or circuit breaker) and has satisfactory earth loop reading then plugging a few lights into it is not going to overload it.
In theory if each flourescent light drew 1 amp then you could run 13 of them from a 13 amp socket though you might have problems with starting current.
I assume you will only be adding one or two so no prob.
yes I have, connected 4 lights x 60watt to a 13 amp plug with a 5amp fuse then i plug into a 13 amp socket as and when required.I will try six at some stage which is well within the safety limits as i understand