Rik I am in an almost identical situation as you - ME/ CFS unable to work since 2002, on IB since 2003, recently received migration to ESA decision and they have stuck me in the WRAG.
Ridiculous really. Especially as I also submitted reports from two doctors and 7 pages of supporting detail in my ESA50 (thanks B+W!). I made many references to not being able to complete the descriptors "reliably, safely and repeatedly" and even referenced reg 35 as my health would inevitably deteriorate as a result of any kind of work related activity.
And like you, I would struggle to manage to attend WFI and would certainly be made worse by the stress and exertion the process would require. The other interesting point for me, is that although I have been unable to do any work for my employer since 2002, I have never been dismissed and remain technically employed, even though I have been found to be permanently and totally disabled by my employer's medical gurus.
Don't think my employer would look too kindly on me trying to find another job via the WFI even if I could!!
Best of luck with your appeal, I shall also be appealing to get into the support group which is where I think I should be, and am grateful to BRO for posting so many really useful links in the same place. Thanks B+W!
