OK. I am assuming that you have disturbed the wires in the bathroom but nowhere else; and that all the lights work except in the bathroom. Let me know if that is not the case.
bathroom pull cord - 3 wires - bare to fixed point -red - com -black to other (i assume l2)
OK. this one is the switch cable. The "red" is live coming from the ceiling fitting. The Black is "switched live" which, when the switch is "on" takes the power back to the bulb. The black ought to be sleeved red, as it is live when switched on. the bare copper is the earth and ought to be sleeved in G&Y.
bathroom light fitting - 2 wires- both containing 1 back, 1 red, and 1 bare
red - isolated in block
Right. I call that two cables, each containing... (etc). The two reds should be connected together but not to anything else. One of them will be the Live from the lighting circuit, the other will be taking the live off to the switch.
bare in the middle of a 3 block
these are the earth wires. They ought to be covered in green and yellow sleeving which you can buy from your hardware shop for about 50 a small packet. If you have a metal light fitting it should be connected to these; otherwise they are just parked.
and 1 black either side
Right. One of these will be the Neutral from the lighting circuit. the other will be the switched Live from the switch; and ought to be sleeved in red as it is live when switched on.
What you do with these two blacks (
never connect them together
) is connect them to the light fitting, one to each wire or terminal. It will probably, if new, have a brown and a blue connection. Or they may be red and black.
If you have a multimeter and can work safely I can tell you how to identify which black is neutral and which is switched live. A neon screwdriver is not very good for that.
Let me know what does not make sense and what does not correspond with what you find.