Alan Holmes writes

I have a large number of these things in my vegetable patch, and most are in
the middle of the strawberry bed, so I cannot dig them out at the moment.

If I just cut off the flowers will that put a stop to new ones appearing?

Depends. At least one species spreads mainly by creeping stems, and it's
most likely that's what you've got. I wouldn't bother to cut off the
flowers, I don't think it'll make any difference.

As they grow tall keep pulling off the tops so they're not giving too
much competition to the strawberries. Once the strawberries are over,
dig up the whole patch, separate the strawberries from the buttercups,
and just replant the strawberries.
--
Kay