The winner of the high-profile contest, similar to the much-publicised Europe-wide Manubuild competition (AJ 27.04.06), will be given the chance to build its designs on a plot in Warsaw, Poland.
The building will be the first to be constructed as part of a Euro 14.25 million (£9.75 million) programme - organised by the International Iron and Steel Institute - to provide low-cost homes around the globe.
Brooks is vying against ten other firms, including practices from America, Japan and Australia, for the prestigious Euro 50,000 (£34,000) first prize.
Contest judge, Australian master Glen Murcutt said: 'We [were] impressed by the ambition and scope of the Living Steel programme and the architectural competition and look forward to its continuing contribution to address the crucial global issue of the sustainability and quality of residential environments.
'Many proposals, and the [final] entries in particular, displayed the potential for steel construction to provide lightweight, open, flexible and refined spaces responding to contemporary urban living.'
The winner is expected to be unveiled next Tuesday (20 June) at the UN-Habitat World Urban Forum in Vancouver.