Yes, political parties here (and in Europe generally) tend to be to the left of the US political spectrum. Even our Conservatives, in the main, believe in our National Health Service (what some here call 'socialised medicine'). But our political parties, like yours, are in reality coalitions of interest groups: the Conservatives, for example, are roughly divided into patrician 'compassionate conservatives' (historically 'one nation Tories' or 'wets'; typically those from a more privileged, aristocratic background who feel that because they have been blessed with a superior status they have a civic duty to try to better the lot of other less fortunate than themselves) -v- nationalist, monetarist, more libertarian/ small government advocates (historically the Thatcherite or 'dry' wing; typically more middle-class or even blue-collar people who've made good or are doing OK; those most likely to vote Republican in the US); there are also Eurofederalist -v- Eurosceptic factions; and, finally, 'modernisers' -v- 'traditionalists', particularly on social issue eg: same-sex civil unions. These divisions overlap to a degree eg: a 'one nation Tory' may well be a social traditionalist whereas a Thatcherite might be a moderniser.
In order to find out where you might fit in, I'd need you to expand on what you mean by 'left-leaning but with conservative social leanings'...sounds like you might be a socially tradional one nation Tory but I'd need to know more!
