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We did something very similar at our last place with two layers of 18mm birch ply sandwiched together with a Formica top (Formica ColourCore with through colour to avoid showing any scores etc.).
We dealt directly with James Latham (http://www.lathamtimber.co.uk/) who did everything including pencil edges to the exposed edges to avoid sharp corners. It wasn't as cheap as an Ikea worktop but was considerably cheaper than any kind of stone worktop and looked very impressive.
Feel free to message me if you need any more info
Accidentally came on the aesthetic solution - laminated birch ply.
Now just gotta find somewhere that will do the size and thickness I need.