There were a significant amount of thunderstorms around the London area around 1.30pm yesterday, affecting anything that had to go through that airspace - as a result of which there were many ATC restrictions. As time moved on, those storms moved east and AMS was very badly affected.
The incoming flight probably just managed to avoid these, or at least was en-route when they started and therefore had some priority in terms of getting in to land. There was apparently an Alitalia plane that was having a fair bit of fun as low as 2,000 feet for 30 minutes, so conditions were certainly not straightforward.
Whilst your flight was not scheduled until 1635, there could still have been knock-on ATC effects from earlier (there's a thread in the BA forum
here which explains some of the difficulties which were still ongoing well beyond that time - the later posts cover 29th May) plus you would have been flying towards an area which was still experiencing quite severe problems. I would think it quite possible that French/Belgian airspace couldn't accommodate you because of everything else having to divert round the storm at AMS, meaning you couldn't get off the ground at LHR.
I would think you'd struggle to make a case for EC261 compensation here, but obviously Duty of Care still applies and A3 will have to cover your hotel, transport from and to the airport and meals.