Outdoor UK cold frame

I've grown in greenhouses, cold frames for decades. It does work. I only use them in the spring and fall to extend my seasons. I think your biggest issue will be autoflowers. I am sure they will grow and do OK but probably not produce record yield. You simply will not have enough light, long enough for them to really thrive. Raising them in a greenhouse is even worse because the glazing (glass, poly sheeting, mulit layer polycarbonate...) all block or absorb a significant portion of light. One sheet of clear glass or one layer of clear poly blocks about 10% of sunlight while two layer polycarbonate blocks about 20%. Best would be to start the plants near the end of this month. That will give them about 4 weeks to grow before the summer solstice (June 21) when the daylight will be it's longest. You want that long daylight to coincide with the plants flowering for maximum yield. Hopefully the weather will be warm enough that you can leave the lid open so the plants can get direct sun (not through glass).