The building is in fact part of the Baptist Union complex in Southampton Row behind, designed by Arthur Keen. The statue of Bunyan on that building is by Richard Garbe, who indeed carved the two kings.
The choice of subject was no doubt prompted by the fact that Edward VII had just come to the throne. Comparing the new monarch to Edward I, a great warrior, Crusader, legal reformer and establisher of parliament, probably went down well.
The images will be totally familiar to anyone who went through an English education before about 1968. Edward I is dressed in chain mail, wears a sword and holds what appears to be a hammer, a reference to his nickname, Hammer of the Scots. Edward VII with his familiar beard holds the orb and sceptre. No sword, though he was a noted swordsman in his own inimitable way.