Technically European law should recognise the transferability of teaching qualifications, meaning that you should be able to take your QTS (which qualifies you to teach in UK state schools) and therefore also teach in German state schools.
However, this often isn't the reality (see my anecdotal evidence earlier in this thread). Many schools are unaware of the law and you are therefore subject to their whims in terms of whether or not they choose to hire you. They can and do use your foreign qualifications as an excuse not to, but (at the risk of sounding too negative) you need to keep trying individual schools that interest you, as I can't believe their recruitment policies will all be the same.
As mentioned elsewhere on this thread, international and private schools should also be available options to you.
To address other points made in this thread, now that I'm able to speak from the vantage point of being a few years down the line from my previous posts: you can get jobs in international schools without teaching qualifications, but it is a gamble, as private school quality can vary massively. I was lucky enough to get a job in a school that suited me (after one false start admittedly!) and I've now been teaching there for nearly 6 years.
Once I'd decided to commit to the profession, I was also able to get my QTS easily enough while still working there, via an assessment-only route. It is ultimately, I think, better to have it, as it widens the pool of jobs available to you (there are still some international schools who only hire qualified teachers) and means you can command a higher salary.
However, it is definitely easier to qualify and get your induction done in the UK before moving overseas: looking into getting my induction done, it appears that so few schools are accredited to do it that your options are severely restricted (even though I qualified in my school, they're not accredited to do the induction, even though it's basically the same process). You're also then in the position of choosing your next school on the basis of where you can do your induction, rather than on the basis of what school is right for you. That, and the schools who are accredited are usually very good ones, so rarely recruit, as their staff retention rate is high. Because of this, I'm actually looking at returning to the UK for a bit to do my induction.