How to tackle this?

Double outlet outside downstairs toilet where electric underfloor heating is to be installed.

I'd like to: 1.Replace current double outlet for a new socket

2.Add switched fused spur

3.Add UFH thermostat

See photo...current socket is mounted 25mm deep onto a wooden stud frame.

25mm isn't deep enough to add the fused spur or thermostat which both need 35mm back boxes and the stud frame doesn't allow enough room for a 35mm box

So do it move the double socket upwards above the stud so that the spur and therm can sit in line to the left?

Tyty