What could cause water to come up from the bottom (upwards) through the tundish?
Amazing it's been a month since I visited this, but I've now had four plumbers, an electrician, a drainage service company, and a previous owner of the home in to figure this out.

Fortunately, the answer lay in phoning the previous owner who was very helpful.

The outflow pipe is blocked (still) meaning that the excess water which is pumped out from the boiler, and perhaps the cylinder, can't escape to the drain. The drain is somewhere under some bricks that look as if they're cemented in, however some are loose and beneath them is a drain. Yes, you heard right, a drain under some paving.

The answer is to find this drain, which I'll find in the next couple of days, and unblock it by calling a drainage service out to use special tools to clear the pipe work. Basically when the boiler is on, the outflow pipe fills up and up until it comes back up the pipe and into the tundish overflow, leaking out all over the floor.

When in doubt, find out where your overflow goes. When you have no idea where it is, phone the previous owner.

Now I'm stuck with many plumbers bills.