Vigorous perennials that shade out weeds, mulched every year with compost and a sharp hoe with a long handle would seem to be your answer.
I think digging over might be actually helping your weeds grow so, yes, I would cover them in a layer of compost. As the topsoil becomes more friable hoeing and weeding gets easier. Also the big gardens plan their borders to avoid bare soil in the summer so all the small weed seedlings are shaded out. Big weeds like docks are so visible that they can be easily targeted.

Apply a decent thickness of rotted stable manure, half-rotted is great on clay but well-rotted is fine too. Get it down asap, and reapply every year any time from late autumn to mid spring. I do mine autumn and spring, about 3cm deep each time, but if I had more muscle I'd do it 10cm deep in late autumn.
It's really good at suppressing the bittercress and also willowherb and stellaria. Unfortunately it does nothing to deter the perennials like oxalis and celandine.
But it doesn't need digging in, just spreading on the top.
If you did dig, that will encourage the annual weeds, whereas a manure mulch will limit the germination of the seeds you've already got, as well as improving the soil over time.

Many thanks for your replies. I tend not to put manure on border as I read once that weed seeds can be lurking in amongst the manure and thought I didn't want to chance introducing yet another type of weed. But if you think it's ok I will do it in autumn as I will have used up all my compost for this year and don't think it will be ready to use again in autumn. Would mike hill soil be suitable also?

That is supposed to say mole hill soil ;-))