Small Crane's-bill on grass which is cut weekly.
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Though you can't judge the size from the picture, I'm sure the size of the flower is too small for Hedgerow Crane's-bill, which as you say is a tall, rather than a prostrate, plant
I considered Doves-foot, but Rose says that has 10 stamens, and this plant has half that number.
The flower is just under 1cm across.
Good point - it could be Small-flowered Crane's-bill then, but that's not a species I'm familiar with.
Small-flowered fits if I only noticed 5 stamens because there were 5 more which did not have anthers. Rose's illustration shows only 4 petals, but the text doesn't specify that and there are plenty of photos on line showing 5. It's very common on greens and beside paths in this area so there are bound to be plenty of people who know it.
Lat/Lng: 51.3765, 0.0082
OS grid ref: TQ398660