That's not what Mr. Memory means.
When you left the JC, they should have given you a P45. Presumably they were remarkably delinquent at doing that. That P45 should have been given to the employer. If the JC didn't get around to doing it before your 4 days of working, you could (and still can) ask your ex-employer for a P46 form that declares your circumstances and enables the employer to deduct tax/NI off your earnings.
When the employer pays you, it will be able to give another P45, stating what it did about tax/NI from your earnings.
You give that one back to the JC, presuming you are re-registering with them.