they WONT do you for no insurance, this is hear say as all you need to say is you forgot to renew and then they can just do you for a fine
as car tax IS NOTHING TO DO WITH DVLA that is also total and UTTER shite too, tax is to do with customs and excise and so the summons would be on another date and not be linked, but like robbing a bank with no insurance
you get the done for the robbery and then the no insurance on another court date
THIS IS FROM EXPERIENCE OF DRIVING A CAR WITH NO INSURANCE AND NO TAX !!!
got done for both and went to court on 2 dates