Did Anthony Trollope's Barsetshire inspire the Archers' Borsetshire?

Barsetshire is a fictional county of England, created by Anthony Trollope for his Chronicles of Barsetshire series published in the mid-19th century. The county town is the equally fictional Barchester.

Borsetshire is a fictional county of England, created for the extremely long-running and popular BBC radio soap The Archers running from 1951 to the present day. The county town is the equally fictional Borchester.

It seems that surely the Archers’ county name must have been based on Trollope’s, but is this definitively confirmed? A website about Anthony Trollope made this claim as one of their "Top Five Did You Know?", but this doesn’t seem very reliable without a proper source or reference.