I think your understanding could be a little wrong here. Insofar as I'm aware, we vote for European ministers to represent us in Europe, and we vote for a government to represent us at home, and the two are unrelated. In fact, I'm fairly sure (without checking) that there's a majority of Conservative Euro MPs in the UK, compared to a huge majority of Labour domestic MPs. So the Euro MPs are far from likely to vote in the direction the government want them to. But then it's also a bit more complicated than that.:)
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I think your understanding could be a little wrong here. Insofar as I'm aware, we vote for European ministers to represent us in Europe, and we vote for a government to represent us at home, and the two are unrelated. In fact, I'm fairly sure (without checking) that there's a majority of Conservative Euro MPs in the UK, compared to a huge majority of Labour domestic MPs. So the Euro MPs are far from likely to vote in the direction the government want them to. But then it's also a bit more complicated than that. :)