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how do you mean about applying for GB? Do you mean for tax purposes GB is not classified as EU?
There are different regs for working inside the EU and outside. It's all part of the double taxation regulations.
If you spend 187+ days anyplace, that's where you're supposed to pay tax. If you're less than 6 months here, you don't have to either. To be more precise, it's where you mostly work. If you're from an EU country and work mostly in another, even if you are not resident there, you pay tax where you mostly work.
There is then an adjustment between the respective tax authorities. An ex of mine now lives in Belgium, but still works in Düsseldorf. She is assessed for tax in Germany, but there is some sort of "adjustment" for living in Belgium. I think it works on the basis of X workdays in D, Y non-workdays in B, so she pays the German FA x/365 her german dues and y/365 what she'd be due in B and the germans pass that on to the Belgians. She did explain it to me in detail, but I was thinking about something else at the time :$
Anyway, that's the EU...
If you are outside, they expect you to sort the tax straight on a 187+days basis, so if you are 187+ outside, you don't have to pay any here.
I think they like to have confirmation here, that you're paying your tax someplace, or they want you to pay here, if you are resident, or a national, because "Sie müssen irgendwo bezahlen!".
In GB, they used to consider that you are not liable, if you spend less than 6 months there, I hope and believe they still do.
I have heard of people getting a statement from the Inland Revenue to the effect that they have "satisfactorily completed their tax returns in the UK", but that meant they had told the IR that they were out of the country, and so didn't pay any tax. The Germans thought they had payed in UK. I have heard the same with Spain.
In fact, in that case, the person had his home in UK, was registered as resident in Spain, and was working here and invoicing through an Irish limited. As the Spaniards take a similar line to UK, he claimed to have confirmations from both that his tax affairs were satifactory. God knows what they'd do to him if he got caught, but everybody was apparently satisfied, and he apparently wasn't paying any tax... and doing 10/4 between here and UK. Don't have proof for it, so it could be a line... An dit would only work if the german's didn't know you were here.
As far as the time outside is concerned, you just have to prove your in and out times with the appropriate tickets. Hotel bills, or hire car / filling station receipts help there too.
I just think being officially resident in Germany would make unnecessary complications. Much better just to have an office here, and sleep on the floor