I'm living in Germany and registered as a Freiberufler and working (directly) for a couple of companies in here.
Now I got an offer for a contract with a UK based company, do I need any extra paperwork?
The answer depends on many things...
If you are working via an Agency, then the picture gets very cloudy, as most will not deal with an overseas company. But as you do not mention an agency, I'm assuming this doesn't apply?
If you are working directly for the UK client, from your location in Germany, then all that is necessary is for your company to invoice the client... and no UK tax or employment regulations apply.
If you are working directly for the UK client, from a UK location, then (in effect) your German company is establishing a UK branch, and is potentially subject to UK tax and also you would be subject to UK employment legislation (in particular the infamous IR35 may be applicable).
I recommend proper professional advice, as taking the wrong option could be expensive in the long run!