I would be tempted to write to HMRC with a list of all employees concerned and maybe a copy of the P11D, explain your mistake and ask them to amend the records
There would be no harm in submitting the P46 (Car) as you say, and write a letter explaining what happened and what you have done.
Going by the way HMRC now work, it may be months before they read your letter and do anything. (In May 2015, I received a reply to my letter of July 2014, about a old payroll query!) Doing both will cover your back and attempt to correct it quicker.