OP: It's been pointed out to me that what you need to charge per hour =
(your desired annual salary + overheads) / your desired annual working hours.
It really is that simple.
A plumber that earns £210,000 per year? Okay. So assume you work a 38-hour week and take 5.6 weeks' holiday and want a taxable income of £210,000, that takes £119 per hour (after you've paid all your expenses). Obviously your hourly rate needs to be higher than this to cover expenses and also to cover time spent travelling, time spent quoting, time spent cleaning the van and buying tools which you won't invoice for, and people who waste your time. You're going to struggle to find customers willing to pay whatever you estimate that final hourly rate to be, unless you are carrying out emergency repairs in London all day every day.
The "Mail" lets it slide that the plumber works 50 hours a week, plus is on call Monday and Tuesday nights. So 78-hour weeks, possibly. Being self-employed, he may not even take a holiday, but I'm assuming 5.6 weeks' holiday anyway. If there are no unchargeable hours and no expenses (accountant, insurance etc), he's probably earning £58 an hour. Not all of us are up to working those kinds of hours. I suppose he won't live to take much in the way of pension, but the "Mail" loves this kind of story for reasons that would be off-topic.
I'm encouraged that you want to do plumbing because you're 'interested'. That's a better reason than the perceived money (and my feeling is that if you never stop studying and changing, your business will always be sustainable). But forget £210,000 a year otherwise you're just running on a hedonic treadmill.