Unfortunately, Appleblossom, now that you've rotovated, the answer is no. Weedkillers which don't have a residual effect in the soil almost always kill through the green, so to speak, so need applying to the leaves and stems of whatever the weed is when the weather is dry, but the soil is moist and the plant is growing strongly. Because you've rotovated, you've now chopped up the roots and stems and spread them everywhere - depending on what the weeds were, you may, in fact, have managed to spread them over the whole area, because the little root pieces may well grow, and the rotovator itself doesn't go deep enough to remove the roots of serious weeds like dock and nettle. You have no option but to dig properly, the whole thing, removing any deep roots as you go, and any pieces of rooty matter lying about. As the soil is light and sandy, it shouldn't be too onerous.

If you can get some old carpet, or better, some of the black plastic used for wrapping haylege, spread it out over some of the garden and leave it for about six months at least, preferably a year. This will effectively kill off everything that will grow up from your chopped up roots.
You can then spend time carefully cleaning the size of area you feel you can manage. If you can clear enough space for a row of second early potatoes you will find this helps to make sure the ground is clean, as earthing up the plants and digging up the potatoes all help to get rid of any weeds left.

Alternatively you can let everything grow back and go over it all with glyphosate, but depending on what weeds you had this might not be strong enough - if you had brambles, dandelions and docks for example. My advice would be to do a smaller part properly rather than trying to do it all at once. Patience it the thing in gardening!