Correct me if am wrong. The SAS provided a Chinook and air crew for Kukhri. That was more like the Multilateral/UN forces pooling resources as such.
The SAS as such were doing their own thing and had been in country for a while. A chuck of the Indian rescue force was sent from India directly for the OP if I remember correctly.
Irrespective - the above was what I was told in the early 2000s and ofcourse things change and nothing is permanent. Though we have zero contact today with UKSF - while regular infantry has done jt training ex of late