existing base for garden shed....break it?

Either. You may want to put in a bit more depth of a foundation, which means digging down the side of the existing.

OTOH a quick and dirty way to get most of what you want is to dig back a little around teh edges, shutter up, and pour a shitlaod of new concrete on top of everything.

Hello john

Concrete blocks, not breeze blocks. Might seem a minor quibble, but it could save you some embarrassment down the builders yard.

Might be worth hunting around for faced blocks. Much more expensive though, and most peeps are happy with rendering over the ugly.

Make for great sheds though.

You can key in, but you need to do the math as to whether the existing is deep enough for whatever height you're planning on, in which case you might not need any further concrete. If not, then trench footings are the way forward, either alongside or break out a trench and go that way.

However... Damp proofing. Concrete sheds don't breathe like wood so damp is more of a problem. It would pay, I think, to rip out all existing concrete and start afresh, putting down a DPM when you lay the new pad/raft. Adequate ventilation also needed (grilles, vents, etc)