Aims. Our aim is to measure the masses and radii of the stars in a newly-discovered detached eclipsing binary system to a high precision (≈1%), enabling the system to be used for the calibration of free parameters in stellar evolutionary models. Methods. Photometry from the Wide Angle Search for Planets (WASP) project was used to identify 1SWASP J063930.33-322404.8 (TYC 7091-888-1, WASP 0369-32 hereafter) as a detached eclipsing binary system with total eclipses and an orbital period of P = 11.66 days. Lightcurve parameters for WASP 0639-32 are obtained using the EBOP lightcurve model, with standard errors evaluated using a prayer-bead algorithm. Radial velocities were measured from 11 high-resolution spectra using a broadening function approach, and an orbit was fitted using SBOP. Observed spectra were disentangled and an equivalent width fitting method was used to obtain effective temperatures and metallicities for both stars. A Bayesian framework is used to explore a grid of stellar evolution models, where both helium abundance and mixing length are free to vary, and use observed parameters (mass, density, temperature, and metallicity) for each star to obtain the age and constrain the helium abundance of the system. Results. The masses and radii are found to be M₁ = 1.1544 ± 0.0043 M_⊙, R₁ = 1.833 ± 0.023 R_⊙, and M₂ = 0.7833 ± 0.0028 M_⊙, R₂ = 0.7286 ± 0.0081 R_⊙ for the primary and secondary, respectively. The effective temperatures were found to be T₁ = 6330 ± 50 K and T₂ = 5400 ± 80 K for the primary and secondary star, respectively. The system has an age of 4.2_−0.1^+0.8 Gyr, and a helium abundance in the range 0.251–0.271. Conclusions. WASP 0639-32 is a rare example of a well-characterised detached eclipsing binary system containing a star near the main-sequence turn-off point. This makes it possible to measure a precise age for the stars in this binary system and to estimate their helium abundance. Further work is needed to explore how this helium abundance estimate depends on other free parameters in the stellar models.