Ask your new payroll department for a P46 form, fill it in and hand it back to them. Since you've had a previous employment in the current tax year, you'll be taxed on a Month 1 basis. This means you'll be taxed on both lower and higher rate for your month's earnings and as a result (possibly) due a rebate next month. How much, if at all, wil depend on your cumulative earnings for the tax year.
One more thing to consider. If you are going to be paid in February and your new employer operates the P46, then the above applies and you'll get your rebate (if any) in March. If your first payroll is in March, however, then your new employer can't give you the refund since your next payroll (April) is in the new tax year. In this case you'll have to apply to the revenue for your rebate.