Okay, I am not an HR or legal person but I have been through this process in various forms as the person seeking a settlement, as someone managing someone out, and in many case, as the person watching my clients handle this.
It sounds to me like whether or not the role is redundant, you are absolutely right that they have decided that they want YOU gone. This is not uncommon in many organisations - they need to cut costs/teams by xx% and they'd much rather do that based on employees they want to keep vs some entirely objective process such as length of service etc. It's also entirely possible that they are using redundancy as an excuse to get rid of you - without having to go through a disciplinary process. In both of these scenarios, the settlement offer is designed to encourage you to take the money, save face etc. And you get MORE money than out of a straight forward redundancy process (with all the tax benefits that come with redundancy).
The reality is that if you fight them and bring legal cases etc to them, the ONLY thing you MIGHT get is more money. They are not going to go to jail, they're not going to get some huge reputational hit etc. Even if there is one person who is driving this, the company have already decided to support your removal, so any push back you bring is NOT going to make life harder for that person but rather, will make everyone agree that the decision to let you go was the better option.
So the BEST way to stick it to them, is to go back with a counter offer that is significantly higher than what they have offered you. I would seek legal advice and explain to your lawyer what you're refusing to do here - which is to explain why it is you think you've been targeted, and why you think it's unfair. Your lawyer can then advise you regarding the potential increase in offer and the language you should use when responding to the offer.
To give you a sense, in a situation like this in financial services in London, I think it would not be unusual to expect to see an offer that is the equivalent to at least 6 months pay, up to a full year, depending on the role and the pay.