Laying vinyl on a uneven floor

I have had my kitchen measured for vinyl but have noticed that there are a few lumpy risen and sunken patches. I know vinyl should be laid on a completely even surface. The fitter says every lump will show up and I should consider getting the floor re-covered with a fine coat of concrete. He used the word "screed" or something like that.
The kitchen measures 16x12. Is this likely to be an expensive job?

I'd recommend something like this

[broken link removed]

frankly I'm surprised that your floor covering supplier/fitter
couldn't help? surely he could arrange it and/or give you
an estimate??