Birch was the second son of Major Richard Birch and was born at Llanrhaiadr, Denbighshire and educated at Giggleswick School, Marlborough College and the Royal Military Academy, Woolwich. He was commissioned into the Royal Horse Artillery in 1885. In 1895 to 1896 he took part in the Ashanti expedition, and in South Africa he served with the Royal Horse Artillery in the Cavalry Division under the command of Sir John French, taking part in the relief of Kimberley, the operations in the Orange Free State and the Transvaal, and being present at the Battle of Diamond Hill. He was promoted major in June 1900, and served in Cape Colony the following year. In January 1902 he received the temporary rank of lieutenant-colonel when he was given command of the 30th battalion of the Imperial Yeomanry, which left Southampton for South Africa four months later. They arrived in early May, shortly after conclusion of hostilities.