Have you tried any weed killers yet? I find that they are very effective against perennial weeds. I've used Roundup & it worked. It doesn't effect surrounding plants if you spray it carefully over the leaves of the weeds you want to kill. I think the ground cover plants are a good idea too. Unless bark clippings are put on very thickly( expensive) weeds can still come up through them , so you still have to kill first.

Might need a few more details but are you able to get among the shrubs ? if so, how easy would it be to literally spot spray the weeds with a small, pump up hand sprayer with a fairly strong mix of roundup or other glysophate based weedkiller. just make sure weather conditions are calm, dry and warmish.

There's no doubt it will probably take a year or two to get things really good but if you keep a little sprayer full of roundup in the shed, then every time you see a pernicious weed, give it a quick spray.

If things are hard to spray, it may be worth getting a pot with a glyphosate mix in and use a paint brush to paint the leaves

Thankyou for your replies. We initially thought weedkiller might damage the shrubs if absorbed into the soil but we shall give it a try by carefully directing onto the leaves as advised. Fingers crossed

The best way to deal with this problem area is to grub the weeds out the best you can, really persistent weeds apply weedkiller, as regards the brambles this is what i do when faced with this problem from time to time on my jobs, grub out as much root as you can any that are very difficult to get out due to close proximity to shrubs/ fences etc, then carefully dab some diesel over the ends of the root this normally works well, once you have cleared the weeds then this area will always be kept weed free only if you periodically through the week scuff and hoe the area which is a five Minuit job if you keep to it.

Bez, glyphosate based weedkillers are inactivated on contact with soil. They will kill only what they touch !!!!!

Glyphosate often doesn't always completely kill brambles though, so be prepared to be vigilant for a year or two as they are very persistent as they have very extensive root systems. Also they are seeding in from somewhere, so you will need to keep a constant watch for new seedlings, which are relatively easy to dig out when young. (I say this with much fellow feeling!)
The toughest brambles do eventually give up if the tops are removed remorselessly every week or two - we converted a bramble patch to lawn this way in spite of having been told that we wouldn't succeed. You can now get glyphosate in a form that can easily be applied by hand rather than spraying, so there is no danger of damaging your shrubs with spray drift, otherwise you need and extremely windless day to spray.

It will kill brambles if you do it strong enough. Sometimes it might be better to cut the bramble back and spray the new growth.

What dilution are you talking about Badfish?