Are there companies that will build furniture for you?

[Catsu]

And what sort of thing would I search for to try and find such a company do you think??
Have ordered a shed/playhouse type thing and wondered if there would be someone I could hire for a few hours/half a day to put the thing up and maybe paint it.... any ideas?

Look in your local paper for a handyman

yes, as MrsSnaplegs says, it's the kind of thing you will find advertised in your local paper.
could try Yellow Pages as well, or if you get a free directory of local businesses through your door like we do.
You're looking for one man (person?) with no overheads rather than a company, I think.
I have definitely recently seen 'flatpack construction' in there with 'gutters cleaned, small repairs, painting' on handyman adverts.