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Hello Tim, I am Keith, one of the experts on Just Answer, and pleased to be able to help you with your question.
You are correct in your surmise that the first 30K of your redundancy payment is tax free leaving 50.878K exposed to Income Tax at your marginal rate. Assuming that you receive 108.574K on 20 July 2017 your employer will pass 70.574K through PAYE. This will immediately skew the PAYE system which will assume that this will be a regular monthly emolument for the remainder of the year and deduct tax accordingly thus over taxing you. If you go on to Job Seekers Allowance then normally the tax account will not be corrected until the end of the tax year in April 2018. If you are re-employed then the correction will take place faster. In the interim you can always ask your tax office to issue a refund of overpaid tax. They will not do this in full, bit you will get something back to improve your cash flow.
In any event 70.574K received in the tax year will be taxed as follows. Your personal allowance is 11K leaving 59.574K exposed to tax, 42.385K @ 20%  and 17.189K @ 40%  total tax 15.662K. This calculation takes no account of any other earnings in 17/18 which, in any event, will be taxed at 40%.
I do hope that you find my reply of assistance.