if you can't conceal the new wiring you could run a 1.0/1.5/2.5 twin and earth cable from the original outlet in plastic mini trunking to another flex outlet or unswitched fused spur unit next to the towel rail. here you would presumably use a surface mounted patress box. wire the towel rail flex to the new outlet.
t+e is recommended for fixed wiring. don't forget to use earth sleeving on the bare earth wire. perhaps some of this wiring can be hidden in the loft space if there is one.
is it an option to run the cable under the floor, and buried in the plaster?
Sorry im getting a little confused now.
Wouldnt a pattress box be the same as the connector (see pic above). Maybe i havent undertood what you meant as im still learning
PS - Thanks for mentioning the trunking, i shall use that