Corbyloon is one of the people on here that know their stuff on JSA, so I don't propose to comment on that. It's kosher.
Severence is a generic term to describe a situation where an employee offers a payment for the employee agreeing to terminate an employment contract. Whether it is taxable or not depends on the terminology set out by the employer in the letter as to the reasons and timescales that describe the termination. It is often of no disadvantage to the employer to set out terms that enable the employee to avoid tax and NI on the payment. For example, the two parties may agree that the employer describes it as a redundancy.
But it isn't always the case and HMRC in any case sets financial limits (The £30k that FF refers to).
See this:
http://www.hmrc.gov.uk/manuals/eimanual/EIM12975.htm