If you have a narrow garden and don’t want to lose too much space, you could vary the border sizes, Narrow on one side say 30-50 cm just for climbers (or none at all) and then a wider border the other side say 90-120cm which will allow more choice of plants and or plant combinations rather than a single row. If you switch which border is narrow or wider through the garden this will also give you changing sight lines.
Don’t feel you have to have a border along the whole length of a fence. A wider border along part of the fenceline will give a much bigger and rewarding impact than a long narrow border. It’s also easier to create a good display as you have a much wider choice of plants to choose from. It will also make those parts of the garden with the narrower or no border feel much wider in contrast.
If you have a garden and a library, you have everything you need.”—Marcus Tullius Cicero East facing, top of a hill clay-loam, cultivated for centuries (7 years by me). Birmingham
Also if you put "narrow garden borders" into Pinterest, that brings up lots of ideas. The main thing is preparation before planting, whatever the border size
Also a border doesn’t have to be straight. Few people actually use the corners of a lawn so a curved bed, wide at the corners and narrower at the centre of the fence will give you more room to plant and give your garden a softer gentler shape instead of a more regimented feel that can come with a straight narrow border of tall plants 😊
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.
Also a border doesn’t have to be straight. Few people actually use the corners of a lawn so a curved bed, wide at the corners and narrower at the centre of the fence will give you more room to plant and give your garden a softer gentler shape instead of a more regimented feel that can come with a straight narrow border of tall plants 😊
Taking that a bit further, when you feel confident to deal with bigger borders, a circular or oval lawn looks good (making the lawn a feature itself rather than just the negative space) and gives you nice deep areas at the corners. Also good to distract from a wonky-shaped garden, whereas straight borders parallel with the fences emphasise the shape, whatever it is.
Doncaster, South Yorkshire. Soil type: sandy, well-drained
I have a narrow border in front of a Laurel hedge, it's been difficult to plant anything that looks pretty and stands out against the dark foliage of the laurel. It's very dry and only gets a couple of hours of morning sun.
I had a couple of white Japanese Anemones elsewhere in the garden that weren't flourishing and I wanted to re-do that particular border so dug them out and planted them in the laurel border while I decided what to do with them longer term - they're doing really well and look very pretty.
I also planted an Actea in the same narrow border (before I knew it's preferred conditions I.e moist soil), the foliage isn't spectacular but it's flowers are lovely, white, tall and smell like bubble gum.
Wall shrubs, climbers and rambling roses are probably the best bet for covering a fence with minimal depth of border. Even in full sun many things will tend to grow away from the fence, partly because they end up getting buffeted by the wind.
"What is hateful to you, do not do to your neighbour".
It would also help to know what height the fence is. We're all probably assuming it's a 6 footer, but it could be half of that, which creates the situation @Loxley describes re wind, especially if it's not a double sided fence There could be a dozen trees nearby too, or garages, or house walls. All relevant.
It's a place where beautiful isn't enough of a word....
I live in west central Scotland - not where that photo is...
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East facing, top of a hill clay-loam, cultivated for centuries (7 years by me). Birmingham
https://www.gardenersworld.com/plants/best-plants-for-narrow-borders/
Also if you put "narrow garden borders" into Pinterest, that brings up lots of ideas. The main thing is preparation before planting, whatever the border size
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.
Taking that a bit further, when you feel confident to deal with bigger borders, a circular or oval lawn looks good (making the lawn a feature itself rather than just the negative space) and gives you nice deep areas at the corners. Also good to distract from a wonky-shaped garden, whereas straight borders parallel with the fences emphasise the shape, whatever it is.
I had a couple of white Japanese Anemones elsewhere in the garden that weren't flourishing and I wanted to re-do that particular border so dug them out and planted them in the laurel border while I decided what to do with them longer term - they're doing really well and look very pretty.
I also planted an Actea in the same narrow border (before I knew it's preferred conditions I.e moist soil), the foliage isn't spectacular but it's flowers are lovely, white, tall and smell like bubble gum.
I will try to get a photo later.
There could be a dozen trees nearby too, or garages, or house walls. All relevant.
I live in west central Scotland - not where that photo is...