Have you tried something like CIFF I think that's how you spell it there are a few cream cleaners I use that I am sure would do the job why not try it on a small corner of the unit with a damp cloth and see if it works

Have you tried Pledge Soapy Wood cleaner? It leaves a lovely finish.

There;s a lovely orange scented wood cleaner/polish spray which I use on my old Ercol furniture. I think that I got it from Kleeneze, we have their catalogue regularly and they have some useful things in there.

Was it Golden Oil wood cleanser ?

If so it's available at QVC.

parker and bailey kitchen cabinet cream looks promising

Forget those high priced bottles. Mix paraffin and meths and keep shaking, as they don't like each other. Apply, soak and then remove with an old towel and toothbrush.

Used this with restoring work with old and antique furniture. Worst case, was an unfinished oak cabinet, belonging to my neighbour on which her cleaner had put wax polish, when it should have been left plain oak.....

Not the same ingredients

This depends on what finish the doors have. If this is a hard gloss synthetic finish, which is most likely on kitchen furniture, neat petrol will remove the grease even if the origin is residues from cooking using vegetable oil, which is usually very difficult to remove. I cleaned some much neglected oak doors this way last year. Smell will clear after a few days and then clean often with water based cleaner or protect with a wax polish. As always try a small area first and remember that petrol is highly inflammable. Incidentally petrol is the only substance I have tried which will clean the grease from the inside, and fan, of a cooker hood.

As I have said before any cream kitchen cleaner is good for that I have used it for years on my kitchen doors with no ill effect I just put a little on a damp cloth clean the doors and wash off with the cloth that has been rinsed in clean water and all the grease has gone

Eureka. Actually took my own advice today. Put a small amount of degreasing jelly on a piece of kitchen roll and smeared it on the oak panelled cooker hood cover. Left it for five minutes and then wiped it off three times with clean damp cloth. Blooming amazing and no effort.