It is easy to save 20k before the age of 20 in my opinion if you're attentive with money. You could work everyday each summer and constantly save, do every little thing to earn some extra money and waste none of it like the majority do.
Up to 18, you need to be in education, so you're unlikely to save much. From 16-18 maybe you earn a bit from working full-time in holidays (under-18s wages, probably, as you're a cheap hire) and maybe a part-time term-time job if you're not doing a lot of studying in your free time.
From 18-20, then, you've got 24 months to make best part of £20K. So you need to save up between I guess £500-£800 every month from whatever job you have, if you're working full-time now.
You need to be subsidised by your parents board and lodging, not be studying further education (otherwise you're in debt), and so you'll need a salary of at least £17,000+ I reckon to save at the top end. That would let you spend some money on socialising, phone contract, clothes, commute to work etc.
But you need to be pretty privileged. You need a family who'll willingly put you up still for no money, and you'll need a job you've found in a tough economic market straight away that you finished school.
The vast majority of 18 year olds are basically brassic.