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Cheapo jugsaw at £10.

http://www.screwfix.com/app/sfd/cat/pro.jsp?id=11932

Are these OK for cutting 40mm worktops? At these prices, use once and
throw away!

Yes - but you'll have to throw the worktop away as well. I'm not anti cheap
tools and have quite a lot of them but for jigsaws it really is a case of
expensive is noticably better, very expensive is very much better.

Why the cheap ones cannot get the basics right of supporting and guiding the
blade as near as possible to the work is beyond me but none seem to manage
it.

IMO Bosch blue range is excellent but if you can't afford that either hire
one or buy pne from the green range.