Walker was honoured with election as a fellow of the Royal Society in 1883. However his post at University College ended in 1888 and after that he devoted himself to mathematical research without holding any further jobs.
Walker ay pinarangalan sa halalan bilang isang tao sa Royal Society sa 1883. Subalit sa kanyang post sa University College natapos sa 1888 at matapos ang kanyang sarili na siya mapagmahal sa matematika pananaliksik na walang humahawak ng anumang karagdagang trabaho.