How to deal with a relative's hoarded cash without being accused of money laundering

is there a danger of the family getting embroiled in a money laundering investigation

1. It is perfectly OK to deal in cash, so long as it is legitimate.

2. Unfortunately, the fact is it is possible "questions will be asked".† It is unlikely, but, possible. This is in the UK, 2020, with the specific amount discussed.

3. IF "questions are asked" you are totally, completely, absolutely, 100% in the clear and normal and will face no problems. You will just state "Grandpa hoarded cash."

You will NOT be "embroiled in a money laundering investigation". You MAY get asked one simple question, with no consequences or problems arising.

It's an unfortunate reality of the modern world that in most jurisdictions, the fact is you can occasionally "get asked about" cash transactions. (Whether by the bank due to KYC, the relevant authorities, or the bank at the behest of the authorities.)

This is absolutely unavoidable, unfortunately.

It's just like, say, you will occasionally be random tested for drunk driving.

In your situation you MUST take the cash to deposit it, so, it is unavoidable - you should proceed.

It is completely normal that (unfortunately) you may be queried on it, but, it's totally and completely OK - like being randomly tested for drunk driving.

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† For example, in France once, the bank (at the behest of the relevant authorities) "pulled me up" and asked why the hell I was withdrawing so much cash. The reason was legitimate and simple, to buy antiques, so - no issue.

So, this is all a game of psychology. Banks do not actually care about source of cash, they care about - in decreasing order - their relationship with their government of the nation they operate in, the network of banks they have to also rely on interaction with, and some foreign governments like the US or EU.

Some banks are more well connected and do not actually care about their relationship with their government, as absolutely nothing will change that relationship. You can tell in their behavior, the outcome of any regulatory action or sanction, the pattern of settlements and repeated behavior.

Knowing this psychology, you can understand the nature of the questions they will ask you. Some banks are going through the motions and are simply looking for you not to give them an excuse to flag a transaction. They don't care about the answer, they just care about the wrong answer. They are simply looking for you to become uncomfortable, unforthcoming, too vague, or saying illegal drugs.

Your answer is simply "pension payments withdrawn and held in cash". Under actual scrutiny there would be proof of this, and the imagined ability to present proof is good enough for banks to feel like they have checked the box of compliance.

They don't care about the source of your bag full of one thousand five hundred £20 notes, as long as you tell them a source. But always be prepared to corroborate that source.

Whenever his (multiple) pensions have been paid in, he withdraws most of it in >cash and stores it in envelopes in a safe."

You (or the bank) will have records of these withdrawals which should corroborate the source of the money if you are asked to prove it.

I suspect any attempts to obfuscate what you're doing will merely draw more attention.