SSP isn't very much money and its paid out by the Government. Company might pay you, but get an equivalent sum back through NI.
Legally your employer is not obliged to keep your job open. Maybe the Company Handbook sheds some light on what the company norms are - or ask HR. The best you can expect is that they agree to take on a Temp in the role while you are away. Mention how committed you are, and stress that you were in fine shape before and your consultant predicts a complete recovery (if true).