There shouldn't be any need for you to do anything.
There is a marker on your P45 which tells the new employer to deduct Student Loan repayments.
If that marker wasn't correctly set, or if you didn't hand in a P45, Student Loan deductions may not start immediately. HMRC will eventually write to your employer with a Start Notice, telling them to start deducting Student Loan repayments.
If you didn't hand in a P45, you could ask your personnel department for a P46 form. Box D should be ticked to show that you are a Student-Loan repayer. However, the situation should sort itself out shortly, so there probably isn't anything to worry about.