Unknown Wild Flower

[Raven48]

Hello Everyone

I found a plant yesterday whilst walking on some reclaimed grassland in Stoke on Trent. I have some knowledge of flowers, and plants in general as I worked for two decades as a gardener and have a qualification in Horticulture.

However, I admit to being totally mystified by this one! I tried to take a photo of it, but it was too small and dainty to photograph well, but it was quite distinctive, so perhaps a brief description will do it...

It looked like a grass, it's approximately 30cm tall with single leaves with parallel veins like a grass, spaced approx 5-6cm apart on a round stem. However - and here's the puzzling bit - at each leaf junction, on a single thin stem approx 1mm wide, there is a single, mainly pink flower that looks for all the world like a pea flower! Only one flower appeared to be blooming at once, and I couldn't see anything that looked like a seed pod.
The place it was growing was on flattish ground, greyish in colour - I'd hesitate to call it actual soil! - which as I say is reclaimed pit land turned into a country park-type area. Other plants growing with it were narrow leaved plantains, knapweeds, narrow leaved dock, artemisias and the like.
Any help you can give me would be great, as I'm totally stumped - not for any other reason but out of sheer curiosity!

[Hedera]

It may be a Grass vetchling, they are very dainty.

[Dorts]

I have here a (very poor quality) image of Grass Vetchling that may help.
Dorts.

[leifus]

and another

[Pete Collins]

Certainly sounds like Grass Vetchling to me. A lovely, delicate flower, one oof my favourites.