> I am a highly experienced developer who has recently taken to freelancing.

If you are a programmer (not web designer) what you want is 'contract programming', not 'freelancing'. Your chances to get a direct contract with a big company (i.e. a company that can afford you) are minimal. Big customers don't talk to single persons. They only talk to other companies. You need to offer your service to one of those companies who will sell you to their big customers on demand.