If you are up for a challenge Kate it is an easy DIY job.
Buy 15mm copper pipe at the length required. Purchase two (maybe more) pre-soldered 15mm straight joints. If not already in your tools kit, also obtain a butane flame canister and torch flame heads (usually in a kit at B&Q) with a pot of flux and wire wool.
Drain system from the lowest point of the radiator circuit, which normally is a drain fitting with a drain nut. Cut the radiator piping of the one you want moved, below any pipe bends that serve the radiator. Lay the pipework to where you wish the radiator to be and reconnect using the pre-soldered joints after wire woolling the copper pipe ends to a shine, applying flux, conecting the joint and with the butane torch heat the joint around the indentation of the solder 'ring' and wait for a silver flow of solder to appear at the joint. Once there stop heating. Repeat the process on all joints until job done.
Obviously all new pipework will need wall fixings, I recommend every metre, and the radiator brackets will require refitting in the required position. always connect the radiator up to the new joints and pipework with it already in the required position.
Refill the system with the correct inhibitor (once more all in B&Q)
Hope this helps Kate. Believe me, once you have done it once, you will think how easy it really is.
You save much money by doing so

On the issue of fitting a gas fire; only get a fully qualified and certified gas fitter to do that job.