Hi JonC
Welcome to the forum.
You might want to have a look at the following FAQ which explains where everything is;
www.benefitsandwork.co.uk/guides-for-claimants/faq/forum As a joint claim then yes if you receive NS ESA support and you are eligible to claim UC (remember NS ESA is contribution based and UC is means tested).
Your case is slightly different as you moved from WTC not ESA, the first question I would ask, was you in receipt of NS ESA before you moved/transfered from WTC as it will make a difference if there is a break in the claim.
I would advise you to seek help from your local Welfare Rights Organisation who can take all your circumstances into consideration when giving advice;
advicelocal.uk Gary