My current shower is electric with a cold-water only feed and is
getting rather old. I think it is 7.5 Kw but I'm not 100% sure.

It is unlikely that the electric feed will support a large increase in
power. Your choices are probably to install a new 7.5kW shower, mess around
with the electrics to get a 10.5kW, or mess around with the plumbing to get
a decent shower.

If you post the length of the cable run, the cross sectional area of the
cable and the way the cable has been installed into the building (i.e. run
between floor boards, buried in an insulated wall etc), then it can be seen
if the circuit is already large enough. However, determining the cross
sectional area isn't necessarily very easy. It is probably 6mm2 or 10mm2
cable. It might be as small as 4mm2.

Christian.