I think for many this umbrella set-up is more a status symbol. ‘I’m not one of you lot, I’m self-employed’, but you’re not really; at the end of the day no matter what the title, you’re still an agency driver subcontracted out by someone to someone else. You have no assets and no say in how the agency or umbrella company is run. If you could cut out the agency and hire yourself directly to the end user, then you’d be self-employed. If everyone could have up to 80% take home pay there’d be no one left on PAYE. 
Grandpa:
I think for many this umbrella set-up is more a status symbol. ‘I’m not one of you lot, I’m self-employed’, but you’re not really; at the end of the day no matter what the title, you’re still an agency driver subcontracted out by someone to someone else. You have no assets and no say in how the agency or umbrella company is run. If you could cut out the agency and hire yourself directly to the end user, then you’d be self-employed. If everyone could have up to 80% take home pay there’d be no one left on PAYE.
I’m not saying you’re wrong, but wouldn’t that still make employed, but with more than one employer?
Anyone unsure of their employment status can use HMRC’s online CEST checker to find out if they are deemed to be employed or self employed. Many contractor representative groups maintain that it is not fit for purpose and inaccurate. In fact it is only correct (supposedly) 75% of the time, according to the Treasury, so there are an awful lot of contractors given duff information. It seems HMRC use the CEST results when it suits them at Tax Tribunals but disregard their own creation as “irrelevant” when appellants can prove duff information was given.