Many (most?) countries have working holiday visas. The rules and availability depend on your own nationality and the country offering the visa, but generally they are for under 30's for up to a year. Some have a higher age limit, some are longer (as you point out), and some can be renewed for a second year if conditions are met.
If I'd known about this when I was young enough, I would have spent year in each of a dozen countries.
Make a name for yourself in some industry. The last time I looked for a job (around age 39), I sent out an email newsletter to about 9,000 subscribers and got back serious job offers in seven countries. I was sponsored by a company and immigrated to Austria on a work visa for technical workers. I would have gotten permanent European residence after five years, but returned to the SF Bay Area before that. There are ways to do it.
It looks like for the UK, you have the choice of CAN/AUS/NZ, Singapore, Hong Kong, Taiwan, Japan (pleasantly surprised to see that) and South Korea. There's also summer camp work in the US via BUNAC (which you pay for), but why bother when you can get a visa waiver for 90 days?
Canada, for example has a Working Holiday visa which lets you remain for up to two years, travel and find employment (if you wish). There are restrictions: age, nationality and there are a limited number, but it's essentially a free ticket for 24 months.