CRI with FI(R)
I doubt if you could get both ratings issued at the same time - the Check Ride is different and the Ground School is not quite the same either (from memory). There is more emphasis on Fault Analysis on the CRI - whereas on the FI the assumption is that you are starting from scratch.
What I did was the CRI (in 2007) and then followed up with the FI a year or so later. In theory it should be a case of straightforward credit for the Ground School (again from memory no credit for the 3h Flying). In practice the CAA were not too co-operative. But eventually it got sorted out and I got both ratings.
Having a Flying job to go with them would be another Bonus.