If your employer offers you an alternative job, you will need to think carefully.
The danger is that if you turn it down you may no longer be legally redundant. This would put you in the same position as if you had just resigned, and would mean that you were no longer entitled to redundancy rights such as redundancy pay.
You would lose your redundancy rights if:
You can turn down a job that is clearly unsuitable, but you can also try it out to see if it suits you.
Again there are rules about this:
However if you say the new job is unsuitable but your employer says it is, your employer may refuse you your redundancy rights leaving you to challenge this in an Employment Tribunal.
So you should take advice before you walk away from an alternative job offer (unless it is clearly ridiculously inappropriate). You will be in a stronger position if you at least try it out and give clear reasons for rejecting it, if you find it unsuitable.
In your employer says you have left a suitable job and is refusing you redundancy pay, you will need to make a claim in an Employment Tribunal and show them why the job was unsuitable.
If the Tribunal finds that you have refused a suitable offer of alternative employment you lose your right to a redundancy payment.