Hello and welcome to JustAnswer. I am here to help you. I am reviewing your question and will respond to you shortly.
Thank you for your question.
If you have been given a P45 by your last employer then you would hand that over to your new employer. In this case income does not start afresh.
If on the other hand you have a tax code that says W1 or M1 .. here each month is a independent month. In this case, you would get your personal allowance on a monthly basis as opposed to cumulative basis.
More information on tax codes and their application can be found here
I hope this is helpful and answers your question.
If you have any other questions, please ask me before you rate my service – I’ll be happy to respond.