Pensioner hoarding cash

I would make an appointment with a local branch of her bank to find out whether you can simply deposit this money in her account. It is not something a cashier is likely to be able to handle.

Do you have power of attorney for her?

Does anyone have a lasting power of attorney for financial matters? If so, then they should be the ones dealing with it.

If she has a bank account, the best bet might be to go to that bank and explain the situation (go into branch - the call centre people can really only deal with standard queries - and ask for a private appointment). Is it all in notes? I know that with coins there is a maximum amount that can be used as legal tender. You need to act quickly as this is a security risk and if your father-in-law is keeping it in his own home his insurance is unlikely to cover it should he be broken in to. Ditto if there is a fire.

There may also be an issue if the cash includes very old notes. High street banks will accept them for a certain length of time, but after that it's only the Bank of England that will do it.

You shouldn’t have too much trouble depositing the cash at a branch. One of my family members is a ‘cash hoarder’ and I once accompanied her with a beach bag full of £20 notes (£20k’s worth!) and paid them in over the cashiers desk. In this particular branch it had to be over the desk and not in a private appt room as there are no security systems in the private rooms so not insured to take such large sums in there.
So we didn’t need a prior appt, but about 3 cashiers got involved in counting it!
Obvs there might be a complication in paying it in to the relatives account if you are not power of attorney/ she is not with you, but the actually paying in of that much cash was fine in my experience.

Is there a cut off date for exchanging old banknotes at a high street bank? I'm guessing these will mostly be pre-polymer style

Banks can refuse to accept large quantities of coin.