Recommend a camera...

Hi guys... I am wanting to buy a camera.
I haven't a clue where to start.
First off, for those who don't know, I'm in the UK.
We own as a family a Nikon Coolpix 3200. It has been a brilliant "snapshot" camera and for general use perfect. We are just a few shots away from photo 5,000! The flash is still going good too. BUT, it has an awful time delay when taking pictures (slow shutter speed) and the zoom isn't very fancy. I would like to be able to take moving shots without a 2-3 second delay with the flash on.
I can't have anything to complicated, but while I'm not wanting a professional ulta style camera I'd prefer an upgrade on this:

I'll be buying off ebay and want to spend between about

First off, for those who don't know, I'm in the UK.

I can't have anything to complicated, but while I'm not wanting a professional ulta style camera I'd prefer an upgrade on this:

I'll be buying off ebay and want to spend between about