We have obtained CCD BVI imaging of the old open clusters Berkeley 32 and King 11. Using the synthetic colour-magnitude diagram method with three different sets of stellar evolution models of various metallicities, with and without overshooting, we have determined their age, distance, reddening, and indicative metallicity, as well as distance from the Galactic centre and height from the Galactic plane. The best parameters derived for Berkeley 32 are: subsolar metallicity (Z=0.008 represents the best choice, Z=0.006 or 0.01 are more marginally acceptable), age = 5.0-5.5 Gyr (models with overshooting; without overshooting the age is 4.2-4.4 Gyr with poorer agreement), (m-M)_0=12.4-12.6, E(B-V)=0.12-0.18 (with the lower value being more probable because it corresponds to the best metallicity), Rgc ~ 10.7-11 kpc, and |Z| ~ 231-254 pc. The best parameters for King 11 are: Z=0.01, age=3.5-4.75 Gyr, (m-M)_0=11.67-11.75, E(B-V)=1.03-1.06, Rgc ~ 9.2-10 kpc, and |Z| ~ 253-387 pc. Comment: Accepted for publication on MNRAS (figs. 6 and 10 shown at degraded resolution)