Honestly, I get where you're coming from — that sounds like a super stressful decision, especially with the KCL offer coming in last minute. Tbh, if you're not 100% set on going into diplomacy/NGO stuff right now, then picking the place you vibe with more (like Edinburgh) makes total sense. Being happy and motivated day to day really does matter.
That said, it is worth looking into what each uni offers in terms of societies, events, and links to places like the FCDO, UN, or think tanks. Like yeah, London definitely has way more stuff happening in that space, and being in the city makes networking and attending events way easier. So if you think you'll want to go hard on that path later, it's something to keep in mind.
But if you're not fully set yet, and you really like the Edinburgh course and the city — no shame in going for it. You can still build a strong path from there, especially if you stay involved and strategic. Either way, you'll be alright.