MsJane
The situation with UC may be changing, previously UC took no account of an ESA Fit for Work Decision and you could claim UC and ask to be assessed without problem, recently I have started to posts about an assessment only being done if the claimant can show a deterioration in their original conditions or a new condition, either of which would reasonably result in an award. You will have to see what happens.
So, you can make a claim for UC, present a Fit Note and be excused from your Commitment for four weeks, after this and dependant on the above, you can either ask to be assessed or they will require you to meet your commitment.
If your ESA MR or appeal is successful then the award will be migrated across to your UC claim, although you will have to chase them. If you were not allowed to request an assessment then your award will continue until you are reassessed, if you were then your award will be limited by the result of the assessment although the associated Decision will carry a new right of appeal.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems 
