The Australian system works well, not dissimilar to what’s described above.
You put an offer in, if it’s accepted you pay a small deposit (£1,000 - £5,000) which has a cooling off period of 5 days. Once this happens, neither party can back out of the sale without a very specific reason noted in the contract of sale.
Your contract will be subject to the usual conditions (satisfactory survey, finance, potentially an onward sale) and you will have an agreed period (usually 21 days) to achieve this. Once this is done, you pay the rest of the deposit & the sale goes “unconditional” (contracts exchanged). Settlement (completion) usually takes place 2 weeks later.
People rarely sell in long chains in Australia, if they do then completion is staggered to allow people to move at leisure. Short term bridging finance is very common because of the certainty in the buying/selling process.
The other dreadful aspect of selling in the UK is the searches process. In most countries these are digitised and self service. Waiting 28 days+ for searches to be returned (or 8 months if you’re unlucky enough to be buying in Hackney currently!) is utterly insane.