The problem you describe is due to the solenoid valve not closing properly. When you press the blue flush button, it powers a solenoid that opens the flush valve. It also switches on the water pump. The problem is that when you don't press the blue button, it closes with a spring.
Either the mechanism is a bit sticky or the washer is leaking: could be that a little bit of grit got past the mesh filter. If it is a sticking mechanism, chances are that in a few weeks or months you'll find that it won't flush at all when you press the button. If it was just a bit of grit, it'll probably have washed away and the prblem is fixed.
A replacement valve is about £40 to £50 from Thetford, but you can buy a suitable replacement on ebay for about £2, though it will arrive on the Slow Boat. Fitting the valve is simple: it just fits in line with the pipe using jubilee clips (or cable ties if you prefer).
However, to get to it, you have to remove the swivelling bowl. That requires reaching in from where the cassette fits, and unscrewing difficult-to-reach screws, then taking out a couple (or is it three? I forget) plastic brackets. They're difficult to get out, and almost impossible to get back in. There are also some curved sliding fittings that are not quite so difficult to reach, but still awkward.
The pipe in the crevices of the bowl go via an anti-syphon valve, which you can simply unclip by pushing in a tab at one end. Don't undo the screw at the other end. You need to remember to put it back as you reasssemble!
If you do decide to change the valve (or get someone to do it for you), first take a good look at the condition of the bowl itself. If it isn't shiny and smooth, bright and white, I suggest you get a new one to go back instead of refitting the old one. They're only about £25 or so.