Could anyone recommend somewhere to buy a 12v electric motor for under £40/$80 including postage? It's for an electric bike, but must have a sprocket already installed, or easily installable, and the main casing cannot be any longer than 120mm
I would suggest you try surplus electronics vendors if you are going to hit that price. Of course it would also help if you have some more specifications in mind for the size of the motor, diameter of the shaft, keyed shaft, current draw, etc. Otherwise you're just bodging. But it would make a good project if they ever bring back "Junkyard Wars."