Really depends on the horse... I always walk trot and canter in both directions and if the horse is hot I halt a lot and leg yield but if the horse is lazy I do a lot of transitions and a couple of lead changes across the diagonal
I always make sure I stretch my horse before riding. I start out by walking her around for 2 minutes without stirrups wig a loose rein. Then I go into a trot without stirrups. After that I put my feet in at a trot. When I've gone over some poles and have done some spirals at a trot, I have finished my warmup. After my warmup I do my cantering and jumping. If she's been good I'll go on a trail and do some galloping with her.
My normal warmup I stretch my horse before getting on, then walk loose rien for 2 or so minutes. If possible walk on hills for 5 min. Then I trot on loose rien for a min, then start to collect her and do transitions, bendy lines, circles and serpentines. Then I do a trot to canter lead on a circle.. canter in to point. Then I do a few canter halt, halt canter, canter walk/trot transitions.
I ride Western so this may not help an English jumper like you, but lunging my horses before riding helps to reduce excess energy and get their legs moving to prepare for a good ride. You don't have to move them up to a canter if you prefer not to waste their energy that you could use to ride, but a good trot is something my horses definitely appreciate, especially after staying in their stall for a night. We usually keep them steadily moving maybe 3 to 5 minutes, let them catch their breath, then tack up. :) once again, not sure if this helps, as I don't do shows anymore.