If your job ends before you have had 28 weeks’ SSP from your last employer and you are still incapable of work, you may claim universal credit (see Chapter 14) and/or ‘new style’ employment and support allowance (see Chapter 11). You will need to send form SSP1 (see 13 above) to support your claim(s).

But if your employer is found to have dismissed you solely or mainly to avoid paying SSP, they remain liable to pay it until liability ends for some other reason.
SSP Regs, reg 4