I don't have a single-colour border, but I have noticed that a lot of the flowers I have that are white go brown before falling - 2 different roses, veronica, lily, cyclamen.
I've got a white-flowered silene under a viburnum plicatum 'Mariesii' which both have/had flowers that go over well, though.
I think you'll want a very few accent plants of a different colour, say silver/purple, but I've seen pictures where the accent colour was gold/yellow/cream and it was horrible.

I'm aiming for white/pale blue/lilac tones for summer flowers in my tiny yard. There'll be yellow in spring as I have to have a few daffs.
I find simple colour schemes much more restful and I couldn't live with riot of hot reds and lots of dark flowers - though I do have dots of purple allium.

I was a bit disappointed with Sissinghurst's white border - I'd go for a few accent plants and Teadrinker's suggestion sounds great.

I think the success of a one-colour border is having varieties in the leaves. I have a white border planted in shade (I think it works better than in sun). It includes an actaea with purple leaves, pulmonaria, a camellia, dicentra, cyclamen, a white-flowered heuchera and several other plants.
A friend of mine with a small south-facing garden decided to go for an all white one. But after four years, she now feels she wants a few blues as it is too bright. I would be tempted to add a spot or two of dark red as well (such as knautia).
I agree with Stera - I was disappointed with the white garden at Sissinghurst, but it's famous because it was the first one.

Thanks for your thoughts. I think I will stick with white and blue, purple and lilac colours. Am going to have a think and move some plants around this autumn.

I've never been to Sissinghurst but fell in love with Gertrude Jekyll's white garden at Bois des Moutiers (at least 20 years ahead of Sissinghurst) when I first saw it in the 1990s. the magnolias there are pretty spectacular as well.

Amsterdam that sounds perfect. I tried to have a blue and lemon bed but didn't have the discipline to stick to it!