Glad you stated where all this is!
It would seem, given that the transformer has a 3-pin plug, just like most of UK appliances, that it would be plugged into a 13A socket. That, so far, makes sense. Mainly as said plug would go into a socket on a ring main, capable of carrying ~30 Amps. And the transformer pulls nowhere near that, let alone 13A.
BUT - Anyone seeing a 13A socket assumes it will be safe for plugging any 13A appliance in. Like an electric fire, for example, capable of pulling all those 13Amps.
That's where the problem starts: the wiring it's attached to, if you go ahead, isn't enough to carry that - it's only for lighting, and were you to do this, someone in the future may plug all sorts in, causing a fire at least. If they were lucky, the lighting fuse/trip on that circuit should blow, which would prevent a tragedy, but then they would need to work out what the problem actually was. O.K. for you, but anyone else living there in the future..?
For me, I'd use a junction box, having cut off the 13A plugs, into the lighting wiring. But you may not be happy doing that, and if the lights needed to be returned, the guarantee has been forfeited. In any case, strictly speaking, a qualified sparky should be doing work on electricity in U.K.
AFTERTHOUGHT: if the transformers have built-in prongs, acting as the plugs (wallwarts), then they will need changing for ones with wires.