Really well done; I enjoyed this thoroughly. You had me sucked into your world and your characterizations from the very first paragraphs, which take us so beautifully inside Toby's head and language. The phrasings are just perfect (like "babes as still messed their nappies"). I'm not British myself, but I've read a lot about British wartime and after, and I'm impressed about how authentic it all sounds -- the class elements and the clothes and especially the class and regional dialects. (Gender history, too -- I can so believe the opposition to women taking NEWTs, for instance).
All the characters are so fully-fleshed out and convincing, from Mrs Moulton down to the louts and layabouts. I like earnest Muggle Toby and determined, strong Eileen who is (of course) good at potions. And I like the way you've imagined the wizarding world and the customs and the magic (details like Eileen's apparating ability being dependent on her state of mind -- and her final "cold calm" that lets her escape.)
I'd love to see what you'd do with the rest of the story, how you might take us from the "proper celebration" to Severus's memories in DH. I'm sure it would be a great and IC ride.