Another data point:

EC261 claim, filed on the morning of 22nd July (as EBD with my number in the form), response received first thing on 12th August, so three weeks time to respond.

They accepted I had a valid claim, and I replied with some further information yesterday. Normally once a claim is processed, subsequent replies are faster but it's been 24 hours now since I replied. We'll see how long it takes for them to finally send the money.