I do not label myself with anything.
However, I am a massive British patriot, and thus support its cultural/political history, and a large part of that is down to pure 'what is sensible'. You will note that the three main parties in the UK are not that different from each other...each of them offer their own "sensible" solutions to various problems. None of which are routed in extreme ideology like you might find elsewhere.
As such there are things I am right-wing about, rooted in British conservative traditionalism, and some things I am liberal about, such as social democracy. Apart of this country is the high taxing of the rich to help the poor. If you don't like it, you can leave, it's been like that and is apart of their socio-political culture.
From our own traditional culture, marriage is an institution for a man and a woman, and it is also the business of the church, which the state shall have no business in. However, as a nation of equality, where the OTT political correctness has eliminated institutional discrimination against homosexuals, people of that orientation have the right to be wed legally in order to have the same rights as straight couples. Therefore, we have reserved civil unions for them, as marriage is the area of the church etc.
Unlike the US, which is a melting pot in its very essence, Britain as a civilization stretches back thousands of years, and thus should not be permitted to be subdued by foreign cultures. I am not ethnically British, but I identify as one, and my maternal family came here, learnt the language and did the whole "When in Rome..." thing. Even my old auntie sees ourselves as "guests", and that if you want to force your culture onto Britain, you can head back to your own country etc.
You can see the mix of left and right wing there, so I don't identify as either.