This is one of my favourite topics. I have until recently been working for a European airline and I have spent a lot of my time and effort in the simulator teaching pilots to keep it very simple when dealing with ATC.
Do we really expect ATC to understand what a double inertial reference problem is or the manifestations thereof? I would suggest that the statement that you have a limited navigation capability or that you can't do an ILS normally might get more of a reaction.
My favourite was the F/O on a LOFT slot who announced that "we are down to emergency level". I promptly asked him what level he wanted to go down to! The answer is to tell ATC that you have suffered an electrical failure and only have the battery left and need to get on the ground quickly. That they will understand.
I don't think this about poor English at all.