I'm wondering just how big this perennials border is - you make it sound like the Forth Bridge...
The time to really tackle it by digging out the plants you want, keeping them safe and then digging the area over, removing pernicious roots of weeds, is autumn. Once the area's cleaned, you can replant the perennials you've kept. You might also take the opportunity to split/divide any large clumps.
For the time being, use a weedkiller which kills 'through the green' - weedol for instance, or glyphosate. So long as you do not get it on the leaves of plants you want to keep, it will not affect what's growing there. If you're spraying, you'd need a non windy day, but it might actually be easier to mix it in a watering can and apply to the plants you don't want. I doubt that one application will kill some of the weeds you've got, and some won't be killed by even three applications, but it will kill off some of them and knock back the rest.

There's a new product on the market, a 'Roundup' gel. I got one to try. If you can't spray for some reason, and you can't move particular shrubs, it might be worth a try. I've put it on winter heliotrope which comes through from next door into my border, where spraying isn't an option. It's systemic.

Thanks for the advice. Must admit it is a far larger area than I should have planned initially, but not impossible! Sounds like the autumn, when I too often have taken things too easy, is the time to get this work done. I think I might move everything I want to keep to some spare garden beds to overwinter and then having killed off the main area of weeds put them back in the spring.
I hate using glyphosate, but having seen its effects around areas impossible to control without it, earlier this year, it seems like the only solution unless I am to spend the rest of my life weeding every day!

I've done exactly what Bamboo is suggesting, Bertie - it's a so-an-so of a job, and it's had limited success, but a lot of the bindweed and couch grass HAS gone. (I'm still working on the awful, tenacious vinca) I moved all my precious perennials into pots and a bed-and-breakfast border for months, starting in March, while spraying the systemic weedkiller on anything that reared it's head. Then I replanted. The trouble is, given a very warm, wet week, all the perennial seeds are germinating like mad and starting the whole process again. It means I've had to be in there every day, weeding by hand, because there are literally thousands of the little perishers, all around my baby plants, and far too close to them to hoe. It doesn't need to be a very big border to make this feel like a mammoth task, Bamboo! I hoped to be stretched out in the sunshine with a cool glass of Pimms by the time we got to June, with all the back-breaking work behind me. No chance!
I am afraid there is no easy answer, Bertie!

I note you mention bindweed, Bertie - in my experience, glyphosate does not kill it off permanently - it simply checks it.

Sounds like I should prioritise my flowers and shrubs one year and marginalise my beloved vegetables! The trouble is I don't seem to have time to do both.

An important thing if you aren't going to do it until the autumn is to make sure nothing flowers and sets seed, or the problem will be with you again next year in full force.
Meanwhile you could cut down the thistles and have a go at the buttercups when you have a little time to spare as they spread so very quickly.

Pure white vinegar will kill the bindweed. I used it in my flower bed, I pulled the bindweed then each day walked the garden when it had one or two leaves I would spray my vinegar on it. This will kill the roots and all, the hotter it is outside the faster it dies. I have been bindweed free for 10 years now.

I'm just wondering about white vinegar, if it works so well for you, Tmh. I've got bindweed re-emerging in my onion patch, and the awful spectre of pickled onions keeps popping up.

I love pickled onions Gattina x wish I was closer Bertie, I would exchange labour for produce of your veg patches! Good luck getting the weeds under control x

We have a massive problem with bindweed both at home and on my allotment so I will try using white vinegar it will be cheaper than any weed killer especially the amount I will need.

Just wondered (being in France) if I could use white wine instead for the bindweed.... so it would come up half cut! (the old jokes are the best!)

I'm afraid it might encourage it instead of killing it!

I have just read all the comments on this thread and am interested on the Bindweed side ... our neighbours do nothing about the wretched stuff in their garden and it now is appearing within my greenhouse and surrounding border ... coming up through the gravel area too! ... As Spritz mentioned earlier ... the Roundup Gel may be the last choice for me ... but I shall try pure white vinegar first ... thanks for the info. Tmh ... :o)

Absolutely can't stand the smell of the stuff so am not surprised it does for the bindweed!

I've been looking on the local supermarket shelves, and there must be 20 different varieties of vinegar - red wine, white wine, apple, etc., but no malt and no white! I'm blowed if I turn our bindweed into gourmet fusspots!

On bindweed, an old lady who used to garden near us in the UK used to use a small bottle full of glyphosate, and she would dip the ends of the growing bindweed in these. She left them for a day and then moved the bottle on to the next bit. Enormously patient work, but she claimed to have rid her rockery entirely of bindweed by persevering.

Gattina, any vinegar will do, basic old brown malt vinegar should be as effective. Vinegar is vinegar, whether its white or brown or whatever, we use different ones in cooking for different flavour, that's all. Spirit vinegar is sometimes stronger though, but all are just acetic acid. Just make sure it is real vinegar though, and not the 'condiment' that fish and chip shops give you as 'vinegar'.

Oh Dear! Has "condiment" reached the chip shops of Britain now? I thought it was only in Italy that balsamic vinegar derivatives had that handle, because at €90 for a tiny bottle, no-one could afford the real thing! I'd better make sure that the malt vinegar I buy in Sainsbury's to bring back here for chutney making is the real McCoy, too. Sad news!