Netty, Speaking from memory from my armchair:
There is a very active Western Riding Club somewhere in the Quantock Hills in Somerset - but my memory escapes me where exactly - try the internet.
There's an outfit which trail rides Western on the western edge of Dartmoor near Tavistock. Superb scenery.
About 5 years ago I rode an English horse on a Western saddle down in Pembrokeshire near Narberth. The wife of the owner taught Western riding. As you wrote, an Englishman riding English on a Western saddle.
But much of what I have heard suggests to me that the main interest in the UK of the Western riders is in showing rather than working and riding the horses in a Western fashion. But that can be fun.
There's a farmer who breeds and sells QHs in Caldicot, Monmouthshire.
There's a chap in Ferndown Dorset who rides, breeds and trains QHs & Paints.
I am fairly confident he could teach any young Welsh Cob D to lope and jog.
But Netty to be honest I am not sure what you are looking for will be found in the Western clubs, especially if locally to where you live there is not an active club.
A well schooled English horse can trot slowly and anyway you could always sit in to a slow trot. It will hand canter if schooled to do so but don't try it on tarmacced lanes.
Likewise, just because a horse is called a QH, that doesn't mean the horse moves 'Western'.
Even without buying a QH, most of the smaller English horse breeds can be schooled to lope but you'll need to be taught to ride Western ie one handed,on a loose rein, uncollected, weight on the stirrup bars, on a Western saddle. True the saddle is more comfy than an Englsh cut saddle
But please pursue your interest - I am sure it will be fun.