Lighting, Light Fixtures, Ceiling and Exhaust Fans - Please help me fix my lights

I followed the exact wiring from the original light fitting. There were three cables each with three wires - red - black - copper from each cable. The switch wires were already marked - one black wire with red tape and one red wire. The light and pull switch both work but the kitchen light now only works when the bathroom light is on. Can anyone help me to fix this myself as electrician charges too much. I am in U.K.

I think you said that at the bathroom switch, there are two connections and three wires. Two of the three wires are connected to one switch connection, and the third wire is connected to the second switch connection. You didn't pair up the right two for the first connection. Try again. There are only three choices for which wire goes by itself. One of the three will work.

I have tried all three black wires to no avail. one connection blew the trip.
There are three cables from the ceiling, each cable has a black, red and copper wire. The switch wires one black with red tape and a red wire were connected as before. To the new light fitting I connected two black wires and two red wires plus all three copper wires to the earth. You said that I had three options but you did not say which colour red or black. Could you be more specific?

Black I believe is what we call neutral here. Try this
At the fixture connect the all black wires(except the one with the red tape) to the black from the fixture.
Connect the red from the switch cable to the red from the fixture.
Connect the rest of the reds and the black with the red tape together.
Connect all your grounds.

:) Thank you for your advice. I tried three permutations with the red wires and hey presto the third worked. I now have independent lights in my kitchen and bathroom.