Basically the current situation is that the first £30,000 of a payment which is paid in connection with the termination of employment is tax free, as long as it is not otherwise taxable as earnings. It sounds simple but can be complicated, here is a government example
The Office of Tax Simplication are currently consulting (until 16th October 2015) on changing the rules one solution is to make it more like redundancy payments, take a look at these examples
There will also be some anti avoidance rules that if you are re-engaged within 12 months in similar job with the same company the payments previously made would become subject to tax and NI.
It looks like we are in for some major changes, its not too late for you to have your say, click on this link