My employer has told me that I am not entitled to SSP or sick pay

Depending on your National Insurance Contributions record over the last two or three years you may entitled to New Style Employment Support Allowance (ESA).  You cannot claim ESA whilst SSP is in payment, however it can be paid in addition to contractual or occupational sick pay.  It is not a means tested benefit so is not affected by savings and most other income that you or your partner have.

You will need a ‘fit note’ from your doctors to confirm the period you will not be able to work for. If there has been a delay in you being able to claim you can request backdating of up to three months.  As part of the claim you will need to go through a work capability assessment. This involves having to complete a questionnaire and in most cases assessment. The outcome will determine if you can continue receiving the benefit and at which rate.

More information is available via https://www.gov.uk/employment-support-allowance