OK, The tiles showed no willingness to detach from the MDF substrate, so a found a piece of scrap 18mm MDF and clamped it to the worktop.
Multi-tool with what I think was appropriate blade hardly scratched the surface.
Switched to angle grinder with diamond blade, much better. A bit scary when I got through the tile and adhesive and into the MDF, as it grabbed the blade somewhat, and my little angle grinder is an awkward sod, as the switch is sprung return, making it hard to get a good two-handed grip.
Nevertheless, It didn't turn out too bad.
Next time I'm in a store and spot some aluminium or black plastic angle I might buy a length, though. It would look a bit neater.
Thanks for all the advice and suggestions.