You do have to give them a P45 and they can work out your pay from your tax code.
You don't have to give a P45. It might mean that your first salary is on the wrong tax band, but that sorts itself out fairly quickly. See https://www.gov.uk/guidance/starter-checklist-for-paye
They also don't know if your tax band is due to salary, loans, deduction, pensions, second incomes etc.
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You don't have to give a P45. It might mean that your first salary is on the wrong tax band, but that sorts itself out fairly quickly. See https://www.gov.uk/guidance/starter-checklist-for-paye
They also don't know if your tax band is due to salary, loans, deduction, pensions, second incomes etc.