If you do it in autumn, you can dig out plants, keep them in buckets or with the roots wrapped for a few hours, while you prepare the border properly. You're right, that border is quite narrow, but you know, most of us probably started out with narrow borders, I certainly did years ago, and over the years, the lawn got smaller and the borders much wider, till they were a minimum of 3 feet from the fence to the lawn, and in some places, 5 feet or more. With deeper borders and a bit of planning regarding height and spread of plants, you can achieve a layered effect, taller stuff towards the back, and so on. It's best if you make some sort of plan regarding repositioning the plants you dig up beforehand, so you can replant them fairly quickly, which means working out height and spread - might help to make a rough plan on graph or squared paper.
I see Allium christophii in the border, and by autumn, you won't know where the bulbs are, so you might want to mark those spots with a cane or something so you can find them later and same is true of tulips (if that's what I'm seeing with the red flowers and black centres). Lupins are a bit risky if moved, they often don't recover very well, so you can either work round it or move it anyway and replace next year if it doesn't do well.
Remember to incorporate some composted animal manure or something similar when you're digging it all over..... and water in well anything you've dug up and replanted.

Thanks Bamboo the red and black flowers are Ladybug poppies

It's a bit of a confused border at present. My idea would be to remove everything at the end of the season, widen your borders and improve the bedding soil. In essence, make a blank canvas upon which you can plan on this winter and plant on next spring.

If they're poppies, they may be difficult to move, the roots go down a long way, so you may have to work round those.

You might consider leaving any of the taller ones that are already nearest the fence, the lupin in particular. Good idea to go round with a notepad and write down which plants you would like to move around. Its so easy to forget what you intended to do when they've stopped flowering and died back. If you aren't sure what any of them are you might like to stick some labels in now.

thanks for all the advice.