It would be quite difficult to design a shower pump that could
prime itself by sucking water up by a column of air, as the
impellors required to pump water are quite different to those
used to provide high pressure air suction.

Why? Many pumps do exactly this.

I said it was difficult, not impossible. I don't doubt that some pumps are
designed to do this, but it is a bit of a compromise for a shower pump. Even
standard non-submerged well pumps, such as venturi jet designs usually need
priming with water. I suspect you could run a standard shower pump above
water level with a separate manual or automatic priming system and check
valves to prevent priming loss.

BTW, for future reference do you know which manufacturers do a negative head
shower pump suitable for suction priming?

Christian.