One thing about English yeast - it is used in a ton of American beer, too. Firestone Walker and Deschutes are both widely-distributed American breweries that use English yeast as their primary strain. There are countless others. Still, some breweries use "American" yeasts to produce "English" styles of beers. English yeasts typically are less dry and more flocculant than American yeast strains and, when fermented at their best temperature (some like it colder than others), they tend to produce subtle yeast-driven aromas. They may also impact mouthfeel, but this could be from the unfermented sugars.
In England most of the top breweries aren't making super-yeast-driven peach-bubblegum-banana bombs. That homebrew we all made when we started that was 1.060+ OG, amber, opaque, and tasted like banana bread had about as much in common with the "ESB" style that we were shooting for as a contemporary India Pale Ale has with Kingfisher Beer.
That said, should you choose an English yeast strain, read what the yeast company says about the fermentation temperature and start at the low end of their recommendation or even a little lower, as the yeast-driven flavors can be exaggerated at the homebrew level. For S-04, Fermentis recommends 59-68F and I would strongly recommend 56-62F. Every time I taste a nasty English beer where someone blames S-04, I ask them and they indicate that they did not keep the fermentation temperature under 64F. Usually these brewers are used to fermenting US-05 or Nottingham at ~68 F and having "no problem," so they assume that S-04 has the same requirements when it doesn't. I am a major S-04 advocate as I like very much that I can ferment with it as cold as 54F and that no D-rest is needed when fermented in the high 50's to low 60's. Many yeast strains (Ringwood) need both a cool fermentation and a warm D-rest to produce great beer.
Additionally, if you are choosing a known low-attenuating strain, try using 5% simple sugar - I usually use dextrose, but plain table sugar works fine. I understand the temptation to mash super low (~148F) instead, but sugar is what the English use and it is more reliable, IME, than ultra-low-temperature mashing.