I am intending to replace my existing thermostatic mixer shower (Mira)
as it continually drips, despite having had a complete set of
replacement washers.

I have been looking at the grohe g2000 thermostatic shower which is on
offer at plumb center for £150.

In the technical instructions for the shower

http://www.grohe.co.uk/icms_dyn/pars...d=733&id_lc=25

it states:

Thermostat mixers are designed for hot water supply via
pressurised storage heaters and, utilised in this way, provide
the best temperature accuracy. With sufficient power output
(from 18 kW or 250 kcal/min), electric or gas instantaneous
heaters are also suitable.
Thermostats cannot be used in conjunction with nonpressurised
storage heaters (displacement water heaters).

Currently the shower is supplied via the tank in the loft and the hot
water cylinder. The house is three stories high so there is quite a bit
of pressure.

Should this type of shower work? I don't really want to go to the
expense or bother of installing a pump,

The current flow rate in the existing shower is quite sufficient.
Although I don't think the shower is set up properly as you need to
have the cold water tap in the sink running to enable the right
temperature. (Another reason to replace in these drought conditions.)

Any advice appreciated.
Tim