A permanent cloud cover is tricky
To have a stable cloud cover you would need either much higher evaporation, or something that causes a higher rate of coalescing (and at lower water saturations). The former requires higher temperatures and is unstable (higher temperatures cause further evaporation etc., until you get a "runaway greenhouse effect" and cook the planet). There is an equilibrium factor given by the fact that more cloud cover raises the planet's albedo, leading to a loss of incoming solar energy; nobody knows for sure whether pushing the equilibrium from its current position to another can be done, and whether such a new equilibrium exists.
Increasing cloud formation can be done through very fine dust (volcanic dust might do), or through other mechanisms such as cosmic rays.
Both mechanisms, as well as a large cloud cover, are at risk of making the Earth uninhabitable in the long run.
However, the Earth's entering a region of space with stronger cosmic ray background, and/or a weakening of the Sun's protective solar wind envelope, would result in a cloudier planet. This too risks triggering a runaway effect, but this can probably be handwaved away (the equilibrium would simply move towards a more humid, hotter planet with higher albedo).
Or... rogue silicon butterflies
The trick here is that what is gloom for a human eye is not necessarily a big issue for most vegetal life-forms. Yes, tomatoes and other plants using mostly lycopene and $\beta$-carotene would sort of get it in the neck, but lots of other possibilities remain.
Basically you need something high enough in the atmosphere - 4000 m, unless you want light to reach the tallest mountains - that will heavily absorb in the 460-630 nanometer range, where human eyes do most of their seeing. The line that interests us here is the blue one for scotopic vision, since photopic (full daylight, full colour vision) isn't going to do much good anyway.
As to what... several doped silicon compounds have a pretty sharp absorption area in that range, and can harvest solar energy; indeed, there are applications where the invisible wavelengths are harvested, to build something that is both a clear window and a solar panel.
All that remains is picture a self-replicating autonomous system that uses silicon "butterflies" to harvest energy -- in the wrong part of the spectrum. It could have started as a means of reducing the global warming and solving the energy supply problem, until the frequency switch turned it into a nightmare.
There is a problem here, however, no matter what kind of hazing material you come up with.
A lot of energy is going to not reach the ground, which means global cooling on a worrying scale - global glaciation scale, even.
Perhaps you could explain it off the other way - the global shield was designed to cope with an increase in the solar constant. When the necessary doping materials were exhausted and the shield started shifting frequency, the part of the program that controlled the energy balance remained in effect, and the required heating is now coming mostly from the near infrared and red wavelengths.
Vitamin D deficiency is going to be a big issue though.