Yes it will.
Most vegetable won't grow well in complete shade, but there are a couple that will tolerate more than most. Lettuce, and peas in the summer months, will do well in partial shade.
Tomatoes, eggplant, green beans, green peppers can all grow in partail shade, but nothing related to food will grow in heavy shade.
Wild violets grow well in full to partial shade. They will spread nicely.
Lavender is a Meddeterranian plant and is better grown in full sun.
Mandeville's prefer sun. They grow best in full sun. However, some people have had success planning in partial shade.
The UK does grow broccoli. A variety known as Calabrese Broccoli is the easiest to grow. It also has a shorter season.
Wild huckleberries grow in forested areas with partial shade. Domesticated western huckleberries are happy and produce well with full sun, or in partial shaded gardens.
Yes broccoli makes your hair grow
No, wild geraniums do not need shade even though yes, they do need it! The flowering plants in question (Geranium maculatum) grow along forested and wooded edges and in forested and wooded clearings and open forests and woodlands. They optimize partial shade and partial sun or, in the case of moist, well-drained soils, full sunlight.
sun/partial shade to light shade
Carrots prefer a sunny site, but they can be grown in partial shade.