of course they have the right to bednobs, any application form for any job will ask if you have any previous convictions and they can ask you to have a CRB check done
http://www.crb.homeoffice.gov.uk/default.aspx
"This service enables organisations in the public, private and voluntary sectors to make safer recruitment decisions by identifying candidates who may be unsuitable for certain work"
So, if money was involved for example would you want to know if the person you employed was an habitual theif