Your tax position depends on several factors. If you are contractually entitled to the payment, then it will be subject to tax and NI. This covers your salary, including gardening leave, contractual bonuses and payments in lieu of notice. If the payment is non-contractual, the first £30,000 is tax-free.
Examples of non-contractual payments include compensation for unfair dismissal and payments of statutory redundancy.
Turning to the share scheme, I assume that the shares are held under an approved SAYE share option scheme. If so, then on redundancy you will normally have six months in which to exercise the option to buy as many shares under the contract as possible. No tax or NI liability will arise on shares either already purchased, or bought within six months.
On the sale of the shares, capital gains tax will be payable in the normal way.