Both Eugenius and his elder brother, John Brannis, were born in Gloucester Terrace, Shoreditch, London to architect and surveyor John and his wife, Susanne. He attended schools in Brighton and at Euston Square. Fascinated by engineering from a young age, he would often visit major engineering works being built in north London. While still a boy he submitted a design for a passenger carriage to the London and Greenwich Railway company. His innovation, to place the wheels beneath the carriage as opposed to the side, thus freeing more room for the passengers was adopted by the railway.
On his return to England from India, Birch brought his global experiences to bear on the developing English fascination with seaside holidays, specifically the construction of piers. With the railways now allowing easy and cheap access to the seaside, and the known health benefits of clean air, businessmen in coastal towns were competing against each other to create the longest and most ornate piers to attract the greatest number of tourists. In 1853, a group of Margate businessmen approach Birch to build the first screw-pile pier in Britain. In its design and construction, he brought two innovations: firstly, stylistic innovations directly influenced by his travels, and secondly, the adoption of screw blade added to iron piles making for a deeper and far more resilient base support. The result was a stylish and resilient Margate Pier, which survived storms and two world wars until it was destroyed by a storm in January 1978. The pier's foundations survive to this day, despite direct attempts at demolition. The Margate pier led to a series of new commissions, which eventually ran to 14 piers in total, the most famous of which is the West Pier, Brighton. His effect on pier construction techniques can be measured in the fact that, from 1862 to 1872, 18 new pleasure piers were built, the majority using screw piling. His last pier was at Plymouth, opened in the year he died, 1884. In the BBCcomedy radio series It Sticks Out Half a Mile, Birch is given as the builder of "Frambourne" pier.
Later life
Later in his life, particularly during his travels, Birch produced numerous watercolour paintings, particularly those of Italy, Egypt and Nubia during a tour taken during the winter of 1874–75.