We did! Last winter. Very similar layout to yours too. They knocked through the back wall and turned the boiler off on the first day of snow here, brrrrrh. They boarded it up with insulated board and hung dustsheets overnight to try and keep the cold out as much as poss. They took the room entirely back to brick, blank canvas and moved everything/started over. They dug out the floor too and laid damp course, membrane, so while they were at it we had wet underfloor heating installed too so we don't have a radiator in there now either.
They did it remarkably quickly really, in the grand scheme of things, and seeing the daily progress was great!
We definitely use our garden so much more now because we don't have to access it from a dingy side path, but directly. And I can see the kids easier while I'm cooking if they're out too. And the doors bring in so much light, and kids can see into the garden from the warmth of inside now too which is great for watching birds, cats, snails on the window, weather etc etc.
We didn't need a structural steel or anything like that.
Took them about 7 weeks all in, but we had a lot of other stuff done around the house at the same time too so probably could have been quicker. Also we lived on site throughout, my DH, me, and 2 kids then 3y and 7m.
We had our fridge, microwave, toaster and slow cooker plugged in to our front room. Which is also where we played and relaxed and lived, essentially. Felt a bit bonkers at the time but worthwhile.
It was a very spenny project for us. We don't intend to do it again so spent more than we might have otherwise.
Good luck!