Well when we talk about social democracy in the UK, generally speaking, we just leave the 'democracy' bit out, and say socialism. So when we are talking about our own political situation and say socialist, we mean social democratic. The prospect of losing or seriously altering our democracy such that it could be considered anything close to authoritarianism is not particularly imaginable, so we just take it for granted, and leave it out. It's more of a semantics issue than an ideological one, fed by the norms of our political culture. A bit like how we usually just say Britain instead of Great Britain.