We demonstrate temperature-insensitive strain measurement in a carbon fibre composite panel using a sensor based on broad-band interferometry in highly-birefringent optical fibre. The sensing element forms an unbalanced Fabry-Pérot cavity in the measurement arm of a tandem interferometer. This is interrogated using an LED source and a scanning Michelson interferometer, producing three distinct interferograms, two of which relate to the group delay (GD) of the eigenmodes of the sensing element, the other providing a zero-OPD reference in the scanning interferometer.We measure the GD of each interferogram by dispersive Fourier-transform spectroscopy (DFTS). Changes in strain and temperature in the measurement fibre affect the group delays of the sensing interferograms, but do not affect the zero-OPD interferogram, which is therefore used as the origin for group delay measurements. We determine a linear transformation relating the measured group delays to strain and temperature. Inverting this transformation then provides a means of recovering strain and temperature from measurements of group delay. We apply this technique to the simultaneous measurement of strain and temperature in the composite panel. Typical measurement errors are 7 pstrain and 0.7 K. The measured values are independent, and the strain values show no evidence of thermal-apparent strain.