I am an athletics photographer, and I have a dilemma. First off, I use the 5D Mark II body. Currently, I own the 100-400mm f/4.5-5.6 USM II, and I LOVE it... except for indoor photos. Before I purchased this lens, I used the 70-200mm f/2.8 for indoor volleyball and the photos turned out great, but I needed the 400mm for other outdoor sports. But recently I went to another indoor game, and the quality with the 400mm is just terrible. I'm considering swapping out my 400mm for the 200 with a 2x extender, so I can get those indoor shots. But will the slow auto focus with the extender be too drastic for outdoor sports like soccer and horseback riding (I also ride)?
I would sell advice to sell all the current gear and get the longest lens with the highest aperture you can afford from Canon and if possible stick with primes, like the Canon EF 300mm f/2.8L IS II USM, as long as it fits your budget.
You won’t be disappointed their performance for indoor and outdoors sports, but it’s pricey.
Have you considered keeping the 100-400 and buying a used non is 70-200 2.8? I found several in the 500£ price range on ebay and given the shutter speeds needed for sports you should be ok without is
Pick the lens with the best image quality.
The rest is technique. Auto focus has its good and bad points. For action, however, think in terms of focus zones and prepare for your shooting with auto-focus off for better reaction time.
As the distance changes, re-focus and shut AF off again.
My first job as a newspaper sports photographer was boxing and my friends were the depth-of-field and my powerful short duration flashgun.
I'd probably start by upgrading your camera body. The 5D Mark IV's low-light performance is quite a bit better than the Mark II, so you might find that upgrading your camera body to a Mark IV increases the usable ISO enough that the difference in lens speed doesn't bother you anymore. And its focusing system is also considerably better, too.