Good advice from BM as usual and difficult to add anything further.
Just remember that SSP, which is not generous, is for 28 weeks only and after that your Employer, who pays the SSP, will give you a form, which will assist with your claim for ESA.
I do not want to depress you but your employer may be considering your capability for the job, which is a potentially fair reason for dismissal. If you wished to claim unfair dismissal at an Employment Tribunal you would need a minimum of one years service with your employer.
I would suggest co-operation with your employer.