The issue will not necessarily be with the airline but with UK immigration who may take an interest in an under 18 year old travelling alone.

Yes you should have a letter from your legal guardian with contact details in case the officer wants to speak to them. This does not have to be a notarised form but equally not a note scribbled on the back on an envelope either.

You need to be prepared to answer questions like who will you be staying with and how much money you will have.

If you are staying with relatives or other responsible adult have their numbers handy as well.

The aim of the officer will not be to reject your entry into the UK out of hand just because you are young but to make sure you will be safe and they have a legal obligation to ensure that.