Is it really possible for someone to avoid paying child support by quitting their job and relying solely on income from poker and spread betting, given that these earnings might not be classified as taxable income by HMRC?

If he were making that much, he would have quit his job already. I simply cannot get over attitudes and laws towards child support in the UK (I have dual citizenship and only returned as an adult a few years ago). The amount most non-custodial parents pay is pitiful and that encourages men to go out and have even more children they're not supporting. The kids and mothers end up in poverty and the taxpayer covers what little they do get. It's completely normal to encounter people who hurt the ex by not paying child support. There's just no thought as to the welfare of the children or there's an excuse. I do volunteer work with kids in my free time at a facility for housing single mothers in poverty (helping them out with their homework). Most of them never even hear from their fathers and the fathers don't seem to get the kind of social condemnation they'd get anywhere else. People accept it. California certainly isn't perfect, but there are laws in place to ensure that not only do parents pay for their children, the child can't live like a royal at one house (a common alienation tactic) while living in poverty at the other one. The UK is so far behind.