Do people need a P45 to get another job?
No you don't ... and it's even less of a problem when we start the new tax year on 6th April.
When you start a new job without a P45, your new employer will require you to complete and sign a P46 form on which you will confirm that you have no other job nor are claiming taxable benefits. HMR&C will use this form to put you on a Month 1 basis for tax. As you'd be starting out at the beginning of the tax year, then there would be no difference. A P46 instead of a P45 only becomes a problem (for the employee) at the end of a tax year when there has been a period of unemployment as you can't get back your unused personal allowance.
Hope that helps.
Cheers
Whirls