[start of marginal, possibly off topic post]
At the risk of being shouted off, although I am sure this is NOT what is happening here, in certain conditions significant current can be induced in a fully floating cable or metalwork.
Consider for a first example the currents flowing in the parasitic elements in a TV antenna. No connection to either end, but current flows, and removing them alters the antennas performance somewhat!!
Also note that a wire going to earth at one end, will not appear conncted to earth at frequencies where it is a significant fraction of a wave long,
which for mosy houses (10s of metres of wire) is a few MHz.
This is also why power only electricians should only be allowed near the earth wires on a radio transmitter with a helping hand !
Actually it is something slightly dear to me, and ~55,000 others in the UK, as the holder of an Amateur radio licence, that (after passing an exam to show competance) we are allowed to design, build and use transmitting equipment of a few hundred watts, on internationally agreed frequencies for the purposes of self education and training.
Amusingly, if on reads the letter of the latest rules, we can still do all of this except the running af a feeder cable to an antenna at the bottom of the garden (which from an interference point of view to selves and neighbours is by far the best place for it.)
By transmitting indoors, it certainly is possible to induce voltages large enough to light lamps remotely if the wiring accidentally forms a tuned antenna - with the UK tendancy to do loop-in lighting, where live and neutral part company for several metres, this is surprisingly easy, although undesirable, as it represents energy not properly radiated, and also in reverse means that interference on the mains couples into the receiving equipment....
[end of borderline off-topic posting]
M.
