Beames began his career as an apprentice under Francis William Webb, at the Crewe works of the London and North Western Railway (LNWR). Between 1902 and 1909 he was the "Assistant to the Outdoor Superintendent", again at Crewe. Whilst in this position he dealt with pumping, dredging and other dock machinery. From 1909 until the outbreak of the First World War in 1914, Beames worked as the assistant to the Chief Mechanical Engineer, Charles Bowen-Cooke.

Having been recalled from the fighting, during the First World War, he became "Chief Assistant and Works Manager, Crewe Works". Then, in 1919 he was promoted to Deputy CME and, eventuall, CME in November 1920.

The LNWR merged with the Lancashire and Yorkshire Railway, in 1922, with the latter's CME, George Hughes, being made CME of the now expanded LNWR, with Beames employed as "Divisional Mechanical Engineer, Western Division". The LNWR was then grouped in 1923 into the London, Midland and Scottish Railway (LMS) and Beames became "Mechanical Engineer, Crewe".

In December 1930 Beames was made Deputy Chief Mechanical Engineer, under Ernest Lemon, at Derby. Beames retired from the railway on 30 September 1934. He was then active in local politics and was awarded the CBE by George VI in 1946.