I found definite information if it is the other way around - if an employee gives notice and changes their mind, the company may keep them employed or remploy them, but has no obligation whatsoever to do so. Since these laws mostly side with the weaker party - the employee - I cannot see that you would have to accept staying employed.
So the fact alone that they changed their mind and offered to keep you employed doesn't give you any obligation to do so, and doesn't relieve them of the consequences at all. They will have to pay your redundancy pay.
If you decided to stay then it would be up to negotiations. And it is not at all uncommon that a company lays off an employee, pays redundancy, figures out the made a mistake, and then hires them back. It is actually common enough that HMRC has published the tax rules for that situation.
Consider the consequences if it was different: Every single company who gave notice would figure out who found a new job, and offer them their old job back on the last day, hoping that most of those wouldn't let the new employer down, and the old company wouldn't have to pay out.