The message from the Safer Neighbourhoods Team talks about identity card but from what I know you need to have a hawkers or pedlars licence & that is what you need to check. You need a pedlars licence to sell door to door without a stall or fixed location, these are issued by the Police. Some of them may be carrying a hawkers licence ( street trading licence) which may not be genuine. Hawkers licence issued by Council.

If they do not have the correct licence ,Police can seize goods and prosecute. Selling door to door without a licence is a criminal offence. If there are a group of these individuals in an area, the Police should be able to check out their credentials/licence & take necessary action?.