I work for Stack Exchange in Germany (where they have no presence except for me), and I'm a regular employee with all German taxes, social security etc. that entails. These things can be made to work.
From another comment I understand they also have a UK presence. Are you a true-blue employee or a contractor who takes care of their own taxes and affairs, and just issues monthly invoices? If you are an actual employee (in the legal sense), are you employed by the UK or US company, or something else? Do they have to have an address there, or a foreign subsidiary? Presumably there's no German legal entity, so how have they registered there to pay tax?
This is something I'm prospectively interested in doing for my own business, but I'm not sure how I'd make it work from a tax point of view.
The only difference to a standard German employee is this: While in Germany legally the employee owes the wage taxes, they're usually collected by the employer and passed on to the authorities. But the German tax authorities don't like to do that with foreign companies (basically because they can't hunt after them when they don't pay). So from a legal perspective, I pay the wage taxes myself (but the tax office takes care of that as well).
A UK company (or a company of any jurisdiction) can establish a subsidiary in another EU state, in much the same way you could register a NY-incorporated company as a foreign company in CA, but this doesn't appear to be what's happened in this case.