UK customs won't care, unless you look very dodgy / go through the red channel. In Europe, customs is information led, so you don't normally speak to them, just walk through

UK immigration, however, will do. They'll want to make sure that your legal guardians know your travelling, that you have somewhere safe to go in the UK, won't get into trouble, aren't being sent into trouble, aren't running away, aren't being sent into unsafe conditions, aren't being sent to / trying to work, that sort of thing

Notarisation isn't really a big thing under English law (not sure about Scottish?), witnessed statements are more common for contracts, declarations and the like. I guess that enough places use them that the UK Border Force (who do immigration) will know what they look like, but I don't know enough to know if they'd expect a witnessed one as is more normal in the UK

At the very least, you should carry with you details of where you'll be staying in the UK, ideally some sort of letter/confirmation that they're expecting you, something from your guardians confirming that they know + are happy for you to go, and contact details (name + address + phone number) for both ends.

If everything goes well, you won't need to pull them out, but they will make phone calls if they think it's needed, and having numbers + names will make things easier if they have concerns