Smart(ish) waterproof coat

[Hall84]

I'm looking for a black properly waterproof coat that is both smart enough to go to work (I get the train from an open platform) but casual enough to last through the weekend. Still have a small ish child that needs running out like a puppy. I do have an uninsulated coat, which is fine for spring but need something warmer to see me through the autumn/winter. I'm no more than 5"2 and a size 12. Would like something slightly tailored in that it nips in at the waist and don't really want the puffy type parkas if that makes sense. Budget around £150/200 at a push.
Even just brands to browse would be helpful. Thank you!

Didrikson do excellent warm, super waterproof coats. They're not exactly 'smart' but not totally scruffy either - certainly fine for my work...

www.didriksons.com/en/women/jackets/waterproof-jackets/grit-women-s-jacket-2-504578-060

www.didriksons.com/en/women/jackets/autumn-jackets/cajsa-women-s-parka-5-504817-060

Thank you! The casja parka is more what I have in mind. Something like that would be fine for 99.5% at work. I have a posh coat with a brolly that is significantly less practical for the rest.

Uniqlo’s seamless down jackets are so warm and very waterproof! They come in different lengths and I have the middle one. Although possibly a puffer is less smart than you were looking for.

https://www.uniqlo.com/uk/en/product/seamless-down-short-coat-460921.html?dwvar_460921_color=COL09&dwvar_460921_size=SMA001

I have a coat a bit like this at the moment. It doesn't hold up for more than about 10 minutes in the rain but is a different brand. Would you get 30/45 mins without getting soggy on the inside layer.

Yes definitely, it feels like it’s impenetrable.

Thanks! Just a hopeful message in case there's any other suggestions

https://www.lighthouseclothing.co.uk/products/outback-waterproof-full-length-raincoat-plum

I have this, actually found it recommended on here. Very dry.