A question for Muslims from a non-Muslim in the UK?

When I want to give a greeting of peace to a Muslim, I have learned to say: As-Salaam-u-alaykum. I had understood that the response to this would be Wa-alaykum-u-salaam - but most answer me differently. Do I have the greating right in the first place - and what is the most common response. I appreciate that in transliterated arabic, the spellings may differ for the same phonetic sound. Help please.