People throw some odd questions my way!
The only direct train services from London to Edinburgh are with LNER from King's Cross (frequent) or with Avanti West Coast from Euston (infrequent).
Anyone at Waterloo, wanting to make an impromptu journey to Edinburgh would need to get across London first, obviously heading to King's Cross because of the more frequent service. (Two Tube trains, changing at Leicester Square OR a walk across the bridge to Embankment and one Tube from there OR one Tube train to Euston and walk from there OR 59/68/168 bus and a short walk OR a taxi Or a 50 minute walk).
However, if I'd seen a poster on Waterloo Station and then suddenly decided to go to Edinburgh, I might have shortened the story a bit by simply saying "So I took the first train to Edinburgh". I wouldn't actually be lying; I'd just be omitting a bit of detail ;-)