I see that "my uncle William Anderson Esq of Russell Square" is first referred to in the 25 Nov 1818 codicil to William Henry Anderson's 1817 will, in the context of his having been given the benefit of an insurance policy to cover "those supposed debts which caused him so much uneasiness" and that WHA therefore recites having "too much confidence in the justice and liberality of my uncle" to think that he will oppose the executors in carrying out the testator's wishes under the will, namely to apply his net estate to the maintenance of his minor sons Alexander and William Henry (by Sarah Lewis otherwise Noble otherwise Anderson), failing which to hold it on trust for his sisters Caroline & Emily.
Nevertheless William Anderson did obtain letters of administration (with the will attached) in his capacity as creditor on 27 July 1819, William Henry Anderson having been buried at Cheshunt on 7 May 1819 aged 36.