You normally give your employer an indemnity in respect of any tax due on the termination payment. It is therefore important that you understand the implications of this indemnity. A statutory redundancy payment will always be tax free and an ex gratia payment would normally be tax free subject to the limit on tax free payments (currently £30,000 irrespective of what you earn) but the payment must not include things like holiday, bonus or wages or any form of contractual payment in order to be tax free.
Notice pay is more complex. The law on notice changed some time ago so that regardless of whether your contract of employment allows you to be paid notice (rather than work it), your notice pay will be taxable. You can read more about notice pay under the frequently asked question “can my notice pay be paid tax free under a settlement agreement?”