The German and the British system of government is very different. Germany has a democracy whereas the British has a democracy in form of a constitutional monarchy. In the following I'll present you the differences and the commonalities about both Systems of Government.

I'll start with comparing the head of states. In Germany the head of state is the "Bundespäsident", who is called "Joachim Gauck" at the moment. In the United Kingdom the head of state is the monarch, which is for now Queen Elisabeth II.
Both of them have no real power and only do representative tasks like orating or appointing the chancellor.

The next point is the constitution. In this case Germany and Britain are very different. Germany has a written constitution which can't be changed easily whereas England has no written constitution, so it has a body of law and a legislature precedent.

Besides the structure of the parliament is a bit different. In Germany the parliament consists of the "Bundestag" and the "Bundesrat". Anyone over 18 can elect the "Bundestag" and the "Landtag", which is the local parliament of the 16 states. The "Bundesrat" consists of all local parliaments. For some laws both parliaments have to accept it, for other ones only the "Landtag" has to accept the law.
In Britain the parliament consists of the House of Lords, the House of Commons and the Queen.

In addition there's a big difference in the voting. In Germany each party get as many seats as the percentage of votes. In England a party has to get the most votes in a vote region to get a seat in the parliament. That's why there are only two big parties in the UK. Whereas in Germany the little parties have a better chance to get into the parliament.

Finally the last point is the distribution of the power. In Germany some parts of the laws get's decided in the whole country by the " Bundestag" and some parts get decided in the states by the "Landtag". In England some powers got devolved to the national assemblies.

Finally I have to point out that the political systems of both countries have the same core, but they are a bit different in all points I presented.