If you didn't register as Freiberufler or Selbständige at Finanzamt, you are none. Legally you are Schwarzarbeiter (illegal worker), at least as far as Germany is concerned. For both of them, you will need a work visa that allows you to work independently while being in Germany, and you need to inform tax authorities that you intend to work as a Freiberufler. Then, tax authorities will send you your tax number, VAT number, and from then on you would be reqquired to comply with the German law regarding doing your business. In any case, you will need to figure out how to do your taxes, retirement insurance, health insurance and so on.
There's no such thing as "I'll work for my company in England for a few months while being located in Germany". Of course you can do it without all of the above, but then you are basically breaking the law.
If you don't know how to do it, your best bet is to just talk with a German tax advisor that could help you filling out all the forms and registering as either Freiberufler or Selbständig. Many cities in Germany also offer free of charge consulting (in German, but some of the consultants may speak English) for people wanting to be self-employed. Similar support you can get from German Chamber of Commerce in some cities.