[3] As mayor, he is credited with having finalised the decision to construct the (then) new Brisbane City Hall at Albert Square (now known as King George Square), by selling the alternative site in Fortitude Valley to the Catholic Church who proposed to construct the Holy Name Cathedral on that site.

[1][4] Jenkinson was a candidate for the state seat of Brisbane in the 1915 election but was defeated by the sitting Labor member Mick Kirwan.

[5][6] Jenkinson was a candidate for the state seat of Toombul in the 1923 election but was defeated by the long-serving sitting member Andrew Petrie.

[7] When Andrew Petie retired at the 1926 election, Jenkinson again was a candidate for Toombul but was defeated by Hugh Russell.

[8] Undeterred, Jenkinson was a candidate for Toombul in the 1929 election but was again defeated by Hugh Russell.