Most of my favourites mentioned - I loved the Office when I was younger (got amazing memories of crying with laughter whilst watching with my cousins, particularly as we were younger and the humour was very risqué for us as impressionable tweenagers).
I would say the Thick of It is possibly funnier but owes a lot to the Office. Also love Blackadder, Inbetweeners, Friday Night Dinner, Black Books, Gavin and Stacey, Motherland
I like the US version of the Office too, and Parks and Rec, Brooklyn 99 - all of the same ilk with some of the same writers involved. But my favourite which nobody has mentioned is 30 Rock, Alec Baldwin steals every scene. You need a decent knowledge of US TV, stuff like the talk shows and SNL, and I think the references were too obscure for the UK audiences which is why it never took off here. But I could watch it again and again, it’s definitely edgier in its humour that the other US ones I’ve mentioned.
On the whole I think people on this thread who have listed similar shows probably have the same kind of humour. I also think the intersection of the Venn Diagram connecting these kind of shows and Mrs Brown’s Boys is empty!!