As others have noted, the 4 months of living expenses requirement can be quite excessive. I've seen similar advice in the past and can't help but recall my personal anecdote of starting a company with barely enough money for one month of expenses. What is far more vital to one's success as a solo contractor is not having savings, but having guaranteed future revenue generation – clients with signed contracts. As the…
So this advice is based on that, but obviously if you're good and marketable, you'll probably be OK. I myself really became a contractor after a relationship breakup when I was in about over £3000 O/D, a mortgage to pay and about £4300 credit limit.
Discussed this with agent, they agreed to pay me the day they were paid and I drove 400 miles for a contract which wasn't actually signed by the client yet. Luckily, they were happy to see me on the Monday, and I got paid at about £4200 into that limit.
This was 2 years ago. Now I probably earn 5+ times my highest perm salary, so in my case the gamble was super worth it, but if you're not somewhat charismatic and decent at your job with a marketable skill, it could go the other way.