I need a low profile extention to the exsiting power cable so it can run along the skirting to the mains socket.I was thinking of joining flex wire to the existing cable, wrapping the 3 cores with heatshrink, and then wrapping the whole thing with white insulation tape. the guy from maplin told me I could do this but then I''ve heard that this is a bad idea (and probably against UK safety regulations).
What I would do is make an extension up and just plug the heater into that. When you don't use the heater anymore use the extension for something else. Normally you need a Janus plug a normal plug and 2.5mm^2 three core flex. You can solder the wires and heat shrink it, just make sure the solder join is done well. If you just twist it together it might heat up and burn.
Assuming the current cord is rated properly, if you extend it, you will need to make the extension one size larger to avoid voltage drop, and overheating of the wire. Doing what you suggest is likely to produce a stiff section that is awkward to handle. I prefer to have a plugin connection so if someone trips over it or pulls a chair with the leg behind it, it will unplug instead of dragging the heater.