Further to previous comments, Joint Personnel Recovery is the sum of military, civil and diplomatic efforts to recover isolated personnel (IPs). JPR encompasses SAR, Deployed SAR (DSAR), Combat Recovery (CR) , Combat SAR, (CSAR) as well as Special Forces Operations and diplomatic efforts (the last 2 are generally used for captured personnel, but not exclusively so).
The JPR mission undertaken in each instance is dependant on 2 things: firstly, the capability of the nation conducting the mission; secondly, the ability of the IP to receive JPR (appropriate level of SERE training). In other words, even if a CSAR capability exists in theatre, if the individual being recovered is not trained or equipped to receive it, a CSAR mission will not be flown - more likely to be CR.
Whether or not the UK has a declared CSAR capabiility, Uk aircrew are generally trained and equipped to receive it.
Further information can be found in JWP 3-66