Thank you. he main issue here is that if you have been continuously employed at your place of work for less than 2 years then your employment rights will unfortunately be somewhat limited. Most importantly, you will not be protected against unfair dismissal. This means that your employer can dismiss you for more or less any reason, and without following a fair procedure, as long as their decision is not based on discriminatory grounds (i.e. because of gender, race, religion, age, a disability, sexual orientation, etc.) or because you were trying to assert any of your statutory rights (e.g. requesting maternity/paternity leave, etc.). It does not matter whether they say it is because of redundancy, or any other reason - they can use whatever reason for termination they want to and they would not have to follow a fair procedure. So do not get too bogged down with that they are saying is the reason – it does not change your rights in any way in the circumstances.
If the dismissal had nothing to do with any of the above exceptions then you would not be able to challenge it and your only protection would be if you were not paid your contractual notice period, because unless you were dismissed for gross misconduct, you would be entitled to receive your contractual notice period. If you did not have a written contract in place you would be entitled to the minimum statutory notice period of 1 week. Your employer would either have to allow you to work that notice period and pay you as normal, or they will have to pay you in lieu of notice.
In terms of paying you anything on top of that, that is entirely voluntary and down to them. They can indeed make it a condition that to receive such pay you have to sign away your rights for claiming in the future. If you do not agree to this they simply do not have to make any additional payment. In the circumstances you will unlikely have any claims against them anyway so you may as well agree to this for the sake of getting 5 weeks extra pay for nothing.
I hope this has answered your query. I would be grateful if you could please take a second to leave a positive rating (3, 4 or 5 stars) as that is an important part of our process and recognises the time I have spent assisting you. If you need me to clarify anything before you go - please get back to me on here and I will assist further as best as I can. Thank you