My view is that you should see the Grant of Probate or Grant of Letters of Administration. The former will confirm the authority of the executors, the latter will confer authority on the executors. Otherwise, how can you tell you are paying the right person?
As to interest, it would depend on the type of debt it is - there may be a contractual right to interest or a statutory right on the other hand, there may be no right at all. Particularly if there is a GoLoA I do not see how they can claim interest since there is no one to whom the debt can be paid until this document is obtained.
Unless it was a HUGE sum of money and worth arguing over, and unless the entitlement to interest is very clear cut, i would be inclined to not pay any interest. They are going to have to either get the agreement of all the beneficiaries (assuming they are identifiable and of full age) or a Beddoes Order to enable them to bring proceedings without a personal risk of costs. Most executors would be very reluctant to do this on the basis that their best witness is dead. However, this is all rather general and on a more fact specific example, I might change my mind.