Submersible pump priming problem

We've bought an old motorhome (a Swift Sundance 500) that has a submersible pump inside the on-board water tank.  I was a bit surprised as I thought that pumps outside the tank were the norm but having seen the prices of pumps, I'm less surprised now.

Anyhow, when I fill the tank and turn the pump on, the pump motor runs but no water flows as the pump won't prime.  The only way to overcome it is to open the tank and stick my hand in and wiggle the pump around and "push" water into the base of the pump at which point it works just fine.

This is a less then optimal solution if I can't wash my hands first before sticking them in the tank!

Is this a peculiarity of my plumbing or is there a surefire way of priming a submersible pump that I can do without opening the tank?  I seem to recall having similar problems withsubmersible pumps back in our old caravanning days but then it was much easier to just give the pump a little jiggle in the barrel to prime it.

I've tried sucking through the shower hose whilst the pump is running but this doesn't seem to work either (before anyone suggest this).

Tim