My bathroom light was not working so i fitted a new light but it still did not work. I then took a look at the switch, removed the screws seen the jumble of wires and just quickly replaced the screws. However the light now miraculously works. Is this safe/possible?
You most likely had a loose connection by the switch, and when you opened it up you moved the wires around which lead to the wire touching the terminal enough for the light to work again.
Bad connections and arcing can cause heat buildup and possibly a fire. Since this is a light and not a receptacle circuit, I doubt enough current will flow for a fire to occur, but it should still be fixed.
Make sure that the power is off, open up the switch box again and hopefully you will be able to see one of the wires on the switch is loose. If not, look for a wirenut that one of the wires is coming out of. If you can't find the loose wire, check the light again.
Macro is spot on, now that the light works, you should be able to figure which breaker controls the switch and light. Look for something obvious. It is a low current circuit, fire likelyhood very low, but... Be careful, I guess you have no meter and little experience with wiring. What will you do?