No, you can't. As far as I know, the CAA allows all licenses, endorsements etc. to be done overseas, except for the IR. I don't know why, but I can make guess... Weather in Florida is totally different from the UK.
So your JAA IR needs to be done in Belgium or any other JAA country. It cannot be done in the US.
Unless, of course, if you go for the FAA IR. That's a separate discussion in itself. Very short: you easily can get a FAA PPL, based on your (valid) JAA PPL. This means that your FAA PPL is only valid as long as your JAA PPL is valid. With slightly more effort, you can get a standalone FAA PPL. To both of these FAA PPLs you can add an FAA IR. This FAA PPL/IR allows you to fly N-reg (US registered) aircraft in airways, in IMC, on IFR flightplans, all around the world. But it is only valid in an N-reg.
For more info about FAA PPL/IR, search the archives for posts on this subject by Bose-X and IO540. And FYI, there is an effort underway to greatly reduce the requirements for obtaining a JAA PPL/IR, to the approximate level of the FAA PPL/IR, instead of the commercial/ATPL standards/knowledge that is currently required for the JAA PPL/IR. The idea is that this proposal should be in place before EASA takes over flight crew licensing from the JAA, somewhere in 2008. This should make a JAA PPL/IR far more accessible.