Ok yes so due to the length of service and notice required by the employer you are not due full pay during the notice period and would only be entitled to whatever sick pay you are due under contract, which could also just be SSP if your entitlement has run out.
There is nothing stopping you from approaching the employer and asking them to discuss a settlement agreement – the worst is they say no and you get nowhere so you have nothing to lose. But to have a chance of being successful you should have something you can rely on that highlights breaches by the employer and give you an upper hand in negotiations.
For example the termination of your discretionary sick pay. In some circumstances employees can be entitled to full company sick pay for a set period, after which their entitlement will either reduce or expire altogether. Such reductions could either be clearly stated in a contract or workplace policy, or simply be left at the employer’s discretion.
In situations where an employee has been in receipt of discretionary sick pay and the employer wishes to terminate such payments, it may be advisable to give at least a month's notice to the employee. Alternatively, the employer should consider reducing their pay gradually so that the employee does not simply go from full pay to reduced pay or no pay in a short period of time.
Similarly, if medical evidence shows that the employee may be able to return to work in the near future and they have only just lost their sick pay entitlement, it may be appropriate to continue paying the employee for the remainder of their absence. If there is no definitive return date, the employee has already received sick pay for some time and their entitlement has expired, the employer may be justified in terminating discretionary sick pay, subject to giving the employee some notice.
Finally, employers rarely retain full discretion in relation to discretionary sick pay and it is governed by the implied contractual term of mutual trust and confidence. This term generally requires employers to act fairly and reasonably when dealing with their employees. If an employer does not act in an even handed manner, it could breach the implied trust and confidence and give the employee the opportunity to raise a grievance at first. If the matter remains unresolved, they could even consider resigning and claiming constructive dismissal, subject to having at least 2 years' continuous service with the company.
As an additional point, if the employee is considered disabled in law (they have a physical or mental impairment that has a substantial and long-term adverse effect on their ability to carry out normal day-to-day activities) the employer’s actions could amount to disability discrimination.
Similarly, with the stress - a good starting point is to look at The Health and Safety at Work Act 1974 and related statutory instruments, which impose a general duty on employers to ensure, so far as is reasonably practicable, the health, safety and welfare at work of all their employees. This includes a duty to undertake risk assessments and manage activities to reduce the incidence of stress at work. In addition, under common law an employer owes a duty of care towards its employees, the breach of which can amount to negligence.
So these are the points you could use to your advantage in negotiations and try to see if a settlement agreement can be negotiated.