Strange advice, employment contracts in the UK generally have a minimum of 4 weeks notice, while contracts tend to require you to start in a week or so.
It depends on the contract. My first contract allowed me to give my notice to my permanent job (pretty sure it was 4 weeks IIRC). I'm pretty sure some of my other contracts didn't start immediately -- it depends on the job. Also, if you have somewhat specialized skills they might be prepared to wait for you.
It's definitely a high risk strategy to quit your job before you've found a contract.
