I'm guessing the coat must be bespoke as no one has figured out who it is by? Given the tartan dress for the Christmas dinner was spotted just from a shoulder. I'm guessing it will be Catherine Walker, McQueen ect Kate seems to have brand loyalty to an extent.
I didn't realise there was an annual get together this weekend for Kate's birthday, very clever to have the Cholmondeley's there this morning implies they are still in the inner circle without saying anything.