A novel method of producing magnetoresistive oxides is described, which involves low temperature combustion synthesis from a mixture of nitrates and fuel, as applied to Sr2FeMoO6. The method yields ceramics with a fine crystallite size of 100-200 nm and a room temperature resistivity of 200 muOmega in. Low field magnetoresistance (6.5\% in 0.1 T) is enhanced dramatically compared to samples prepared by conventional solid-state reaction due to the efficient intergrain tunnelling arising from the high density of grain boundaries. Magnetoresistance in low fields is essentially independent of temperature from 5-300 K, and it persists up to 350 K, providing the prospect of sensor applications in an extended temperature range.