When the slit is smaller than the wavelength, the single slit diffraction pattern is not visible in the range of angles $-\pi/2$ to $\pi/2$. The diffraction pattern is the Fourier transform of the transmission function, and when the slit is much narrower than the wavelength, the diffraction pattern turns into the Fourier transform of a delta function, a constant. The two-slit pattern turns into a nearly constant intensity, with only a little bit of decrease in intensity of size $1/k^2$ when the two slits are closer than the wavelength divided by k.
Addition as requested
single slit diffraction also works to demonstrate that light is a wave, it is just a little trickier to analyze mathematically because it requires doing an integral, while double slit is trivial, so Young focuses on double slit. Newton had a weird pulsating-particle model for light which could reproduce interference fringes, by assuming that light pulsates regularly between different states, and only some of the states could get through a material. Newton wanted this to be true because he believed matter was particulate, and that the particles interact through the third law, explaining the conservation laws. He couldn't bear the idea that this scheme only worked for matter, and not light, so he tried to shoehorn light into a particle model.
The final proof that light is an actual wave, not a Newtonian pulsating particle, came from the observation of the completely-counterintuitive constructive-interference bright spot at the center of perfect circular disk shadow. At the center of a disk, you get a spot of constructive interference called the "Poisson spot". Wikipedia says that Poisson, who believed in the Newton theory, demonstrated this as a paradoxical consequence of the Fresnel theory of diffraction, but Arago experimentally observed the spot almost immediately afterwards, vindicating the wave theory. No pulsating-particle model can explain how particles at different sides of the disk can conspire to join up exactly at the center--- that must be a wave diffracting around the whole disk.
Of course, we now know quantum mechanics and photons, so Newton wasn't so terribly off. But his pulsations need to be spatially extended so that they make a full diffracting wavefunction, not just a temporal oscillation along the particle path.
Fresnel's paper is here: http://books.google.com/books?id=_0hWAAAAMAAJ&dq=memoir+of+fresnel&pg=PA79&hl=en#v=onepage&q&f=false