In reply to Dan Arkle:
It can take 6 weeks for them to sort out a claim for any benefits now so you won't actually get anything til then at the earliest. I'd weigh up how long it will take for you to recover against how long it will take for the claim to be processed. If you need it for rent/council tax rebate claims, get it sorted ASAP because that will take another 6 weeks after you've gotten the ESA sorted to be processed & landlords don't wait for it all to be sorted now