My in-laws have a power shower that sucks their immersion tank cold
in about 10 mins, so I'm not too keen on them. My parents have an
electric one (ie. pull-cord then instant hot water from cold feed)
which gives reasonable (if not gym/hotel deluge levels!) umph to the
water coming through it.

Well, it sounds like you might have a mains cold supply. If so, a venturi
based shower might be ideal for you. The flow rate is not quite as good as a
power shower (which probably appeals to you!), but it will be much better
than the feeble electric shower. It also means the water is heated by gas at
a fraction of the running costs of electric. So you save running costs,
installation costs AND get a much better flow.

If you don't have a mains cold supply to the bathroom, then a twin impellor
pump might be worth having. This will also benefit bath filling. The final
other alternative is an all-in-one power shower which consists of a single
impellor pump after an internal mixer. If you choose a shower with a flow
control, you don't have to have the full deluge, but you'll still save
loadsa money on water heating and it will be easier to install, as the
electricity can come off a nearby ring main (via a 30mA RCD FCU if
necessary). It doesn't require a 10mm cable run specially for it like an
electric shower.

Remember that the electric shower basically requires a mains cold supply
too. So if you don't have one handy, the installation issues for it are even
greater.

Not having to worry about central heating warming up a tank first
would be a bonus.

Try setting the timer to heat the tank for you! In fact, running it close to
24h a day (or off from 23:00-5:00) isn't a bad idea on a modern insulated
tank. The temperature drop during the course of a day isn't sufficient to
make not doing so much more efficient.

Christian.