There's no easy answer to this question and I'm afraid that my hunch would be that you will struggle to switch the mortgage to another lender.
Mortgage providers will take some benefits into account, especially if there is no indication that the benefit payments could come to an end.
For example, Nationwide will take incapacity benefit and disability living allowance into account in the same way as earned income. But even then, I'm afraid you wouldn't be able to meet its affordability criteria.
One other option I think you should definitely investigate is whether your existing mortgage lender has any other mortgage deals that it can offer to you. This way you can get a better rate without having to apply to a new lender.
You might not get the best deal on the market but this could be an option to cut your costs.