If you are unable to carry out CRB checks, simply insist on references from previous employers.
The law requires you to carry out 'reasonable' identity checks for employees.
You should insist on the following as a minimum:
Photo ID. (driving licence, passport etc.)
Utility bill. (showing name and address, and less than one month old)
Document containing NI number. IE: P45
For employees without a P45, simply fill out form P46. Within a few weeks the Inland Revenue will confirm their status for you.
As for trusworthyness, for employers it is usually just a matter of good judgement and luck that you employ an honest person.
Hope this helps