A word of warning to those who are saying it isn’t an issue if she is 15 and the bf is 16 - it most definitely is and is dedicated as statutory rape.
I wasn't going to contribute to this thread because the first few posts were so helpful, but now we have nonsense being spouted so here I am to set the record straight.
There is no offence of statutory rape in the UK. And the only offence which might warrant that title would be sex with someone under thirteen. A person under 13 cannot legally give consent (if they do, it's invalid) but someone aged 13 to 15 can - it's the activity itself which is technically illegal.
The age of consent is 16 for a reason - and the reason is essentially to make it easier to prosecute adult sexual predators who target young people (mostly girls) and groom them. It is not to prevent consensual sex between younger teens of similar age (and this is made quite clear in the (2003) act).
It is not helpful to think of teenagers as children. The very fact that they are capable of having sex demonstrates that they are not. In this situation a legal definition of 'child' (which exists to provide under-18s with benefits/protection) is inappropriate.
OP - please do not tell either the father, nor the boy's parents. A healthcare professional would not be allowed to, so why should you? To do so would be a breach of trust and confidentiality. This is a private matter between the boy and the girl. You only found out by accident so, other than being supportive (as you are), you should not interfere.
Regarding the doctor. Good that you are supporting her, but have you asked her if she wants you to go with her? If she does, then of course that's fine, but does she know she can go on her own? She might prefer a private consultation. She could even go with her boyfriend - if that's what she wants. And it's entirely her decision as to the type of contraception she uses. As long as the HCP is happy that she is mature enough to understand what is being proposed, she has the right to make that decision.