I think that you will find a lot of information on how to approach it in the BA forum.
Luckily, the UK has these convenient Small Claims courts.
My suggestion would be to write a letter to the UK TG office, possibly SignedFor, where your state precisely your EU 261 claim and request for 600EUR compensation. State that without a satisfactory response within two weeks you will enter a small court claim.
Again, check the BA forum.