How to effectively manage whatever this is growing in the lawn

Lawn is full of this grass type, which is making it look really bobbly and uneven. I don’t think any lawn care has previously been done, meaning this is taking over a large % of the total area (about 100m2)

Is there anything I can do that can deal with this? Or is it just a case of cutting short, overseeding and hoping the new grass takes over? Thanks!