Welcome to the Forum! Great question, I just went through the billions of forums on here on bitless bridles and settled on which one fit me and my horse best too.
Here's a sum up of what I've learned.
The rope bridle you posted is a cross under, same concepts as Dr. Cook's or Nutural, I would recommend you go with either of those two before going with a rope alternative. The rope one in your photo has many knots which each lay on pressure points - this makes this bridle VERY strong (too strong IMO). I'd personally prefer to put a milder piece of tack on and teach the horse properly how to respond to it. Being an English rider you may be looking for something with a more 'classic' look? Dr. Cooks and Nutural both look like a regular bridle, it takes a minute to notice you don't have a bit ;)
My personal choice was an Indian Hackamore which is similar to what you've got in that photo but not quite.
This is just a nose band that attaches to any head stall (so it can look as classic or as crazy as you like) :) It crosses under, just under the chin rather than across the whole face. I preferred this because, to me, it had more clear turning and stopping power. I own one just like in the photo. Pros were, it's fantastic my mare responds perfectly to it. The part the reins clip to, crossing under the chin, runs through metal rings (as opposed to rope loops) so the release is more immediate. The only con I found is that the material was a little rough, I was afraid of it rubbing her fur (it didn't I was just afraid) so I put fleece on it and it's been perfect ever since :)
Of all the bitless option Dr.Cooks/Nutural and Indian Hackamores are my favorite for direct reining. :) I've also seen some where it's just a rope noseband with rings on the sides - this is probably the nicest I've seen, but may not have the strength you may need?
Good luck - have fun!