Dear me, no. The first point is that if your wiring is of such an age that the lighting circuits have no earth, then you ought to be thinking in terms of a complete re-wire before too long.
A temporary solution is to run a separate earth (properly called a 'circuit protective conductor' or CPC) from your fan back to the main earth terminal in your consumer unit or fuse-box (near the meter). A water pipe should not be used as a CPC because (a) you can't rely on its continuity after plumbing alterations (plastic pipes, Speedfit fittings, etc), and (b) in old wiring there's probably no main bonding to the incoming water service in any case.
For a separate earth like this you will need 4mm^2 green & yellow single-core earth wire. The cable type is called 6491X, but just ask for "4 mil earth". You'll find that it has seven strands, not one, BTW.
Strictly speaking, to comply with wiring regs your earth should follow the same path back to the consumer unit as the other wires in the lighting circuit. However that probably won't be a practical thing to do and ignoring it is a much more minor transgression that not having an earth at all.
HTH