If there is no house, then the bank building society or other financial institution can deal with this under the informal small estate rules. What happens is that if there is only cash, and no shares or property and not tens and tens of thousands of pounds of cash, they will allow the personal representative/next-of-kin/executor of the will to sign a statutory declaration that they will deal with the estate in accordance with the will/rules of intestacy and that they are entitled to do so.
The bank/building societies have a standard form which the person takes to a firm of solicitors and swears on oath. There is a fixed fee of 5 pounds traditionally payable in cash which the solicitor will usually pocket. Many solicitors will do it without having an appointment because it takes two minutes.
Depending on how many potential beneficiaries there are, it may be necessary to open in executors trustee account to keep the money separate from that person’s own money.
Unfortunately, pension funds and insurance companies can be quite pedantic. I would suggest that you told them (better in writing) that all the other institutions are dealing with it by way of statutory declaration under the small estate rules and that you don’t therefore need probate and can they deal with it in the same way? It’s up to them whether they do or not.
I’m afraid that NS&I in a bit of a law unto themselves.
If you haven’t already seen it, this is the form that you need.
As it says, (leaving everything wide open!) They may ask for probate if the customer’s total NSI savings are over GBP5000 although they reserve the right to request a grant for any value.