You can buy AppleCare any time during the first year warranty period, so you don't have to buy it at time of purchase.
You can check your remaining warranty and/or AppleCare coverage here
AppleCare will extend the 1 year warranty for an additional 2 years, for a total of 3 years coverage from the date of your Mac purchase.
It also extends telephone support from 90 days, which is included with your original warranty, to a total of 3 years.
You cannot buy AppleCare again or renew it once it expires.
Neither the Apple Warranty nor AppleCare will cover damage from accidents, spills, etc. They only cover manufacturing defects.
AppleCare+ provides some coverage for accidental damage, but is only available for the iPad and iPhone, not for Apple computers.
Neither the Apple Warranty nor AppleCare will cover batteries that have worn out. They only cover defective batteries.
As to whether AppleCare is worth it or not, that's a matter of opinion. You'll find lots of opinions on both sides, with roughly 75% saying it's worth it. You really need to decide if it's worth it to you. If you want more information, you can search the forum, where you'll find dozens, if not hundreds of threads asking "is AppleCare worth it?" The overall consensus seems to be about 75% in favor of it.
In the UK you have pretty robust consumer protection legislation. Goods must be of "satisfactory quality" and last for a "reasonable period" taking account the goods in question and the price paid.
Example - a literal apple fruit should be intact and free from major bruises (it's allowed to have some, it is a fruit after all ) and last for about 2 days after purchase.
A £2,000 apple notebook should be near perfect at delivery (I'm saying near, because nothing will ever be perfect) and last for about 2 years before needing to be disposed of. If it develops a manufacturing fault (NOT including a problem that is your fault, such as accidental damage) within that period return it to apple and ask them to fix it (you are entitled to a repair at their cost, not a replacement). From experience, unless they have a strong suspicion/can show that you have damaged the notebook in some way they will certainly help. If they don't, get trading standards involved or sue them in the small claims court.
Apple Care in that respect will in those circumstances only probably give you an additional year of "manufacturer warranty" so to speak. Whether it's worth it is up to you.