At the latest transfer fair the only Regiment/Corps willing to accept any sort of downgrading was RA. They were willing to take P3MLD for UAV operators subject to medical review. That was about it. This was before SDSR however, so they may have tightened the reigns.
As dingerr said most units already have their share of downgraded personnel. They want troops who transfer in to be MFD (medically fully deployable). RLC AT trade is short of high threat EOD bods. Not much use doing that if you can't deploy to a high threat environment.
As BM says, no one will take you unless you can deploy. It's always worth asking the question though. You didn't say if you were permanently downgraded or not. Also, bear in mind, even if you are perm, if there is an improvement in your condition you could be upgraded. Word on the street is that unless you are at the upper end of MLD, there are no vacancies. Good luck.