<p>A reactor has an external ultra-violet lamp (1) which irradiates a fluid reaction medium (3). The reactor has a housing (15) around a tubular chamber with an inner tube (2) forming an annular irradiation chamber (26) with a fluid (3) inlet (13) and outlet (14). The fluid flows through the chamber (26) via a transparent helical tube (6,25). The inner tube (2) has a reflective coating. The transparent helical tube has flattened, oval, square or semi-circular cross section sidewalls.</p>