Just a data point for anyone searching this topic...
I was delayed 24 hours just before Xmas and submitted what I assumed was a slam dunk claim for compensation under uk261 which BA threw out citing "exceptional circumstances" a few weeks later.
I filled in the CEDR form online mid January as I was unhappy with BA's bs reply , it took 5 mins maximum. CEDR suggested my claim was valid and today BA reluctantly agreed and asked me to provide my bank details.
The process was simple enough and whilst a little protracted was handled well.
If you're in the same boat I would not hesitate reccomending you use CEDR.