Since your bathroom is rather remote from the rest of the system, it may well cost that to install a towel rail and a completely new pipe run.
But, unlikely to cost that much if the whole system is being replaced (new pipework completely.)
If the upgrade is boiler plus controls only, i.e. NO new pipe runs, then I would go for a simple 150W electric towel rail. Even if there is no socket circuit nearby, it can be powered from the lighting circuit providing that the correct isolation and fusing measures are installed as well.
If you go electric, then please remember that this is notifiable to Building Control (bathroom location.) Alternatively, have the circuit fitted by a "Part P" electrician. No Building Control needed.
Also, an RCD (earth leakage trip) would be needed. Have an electrician quote for you. It should be significantly cheaper than the £600 option.
Or........ have an electrician quote for a circuit & fitting of a wall-mounted fan heater. Heat when you need it. Much more so than a towel rail alone.