Hello,
i would like to know whether "umbrella contract" is the correct and suitable term to be used in an official document (a contract).
If somebody could help me that would be great :)
It is correct and suitable for a particular kind of contract. I don't know the details but contracts like this were introduced by HM Revenue and Customs fairly recently as a way of limiting the business expense a self-employed person can claim: rather than just keeping receipts for everything and getting away with as much as you can, a freelance signs an Umbrella Contract to a casual employer who pays expenses gross (so that the individual freelancer can't claim them again.
But I'm not an expert (though I've signed a few). The HMRC website will probably tell you more than you want to know! Here's a good place to start: HMRC Search
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Thank you! You have been very helpful :)