I also get them on my plot they blow in from other unattended plots.
They are an absolute nightmare and can put down roots anywhere sometimes forming a matt of tiny green plants early in the year.
When they mature they resemble a very small willow herb but instead of the long stem with the pinkish flowers these have side stems also and produce a profusion of floating seed the same way as the willow herb.
I agree with New Shoot that the only way I've found to control them is hand weeding.
I would not let them take over an area because then you would have to deal with the roots.
I've had allotments for a long time in the same area and have only noticed these over the last five years but they are everywhere on our site now.
Good luck
