No. GO and sign on as soon as you stop work. Otherwise you don't get backdated NI contributions. You won't get any money while your claim is investigated, and they won't backdate your JSA payments, but they do backdate your NI contributions so it's worth doing as they count your contributions if you have another jobless period within 2 years.
I made the same mistake in 2002 when I was made redundant with a large payment in lieu that included a few months in advance. I waited three months (thinking I had no claim because of payments) and when I did sign on as unemployed had a battle to get NI contributions sorted. I also found at that time I could have been receiving unemployment benefit which I lost out on because of the backdating policy.