There are two styles called EIPA: the kind of beer that BJCP describes, and the kind you actually see in most pubs in England. I heartily prefer the latter.
Most beers I've had called "IPA" in England were straw to light amber in color (4-8 SRM, or thereabouts), 3-6% ABV (typically about 4.5%), light-medium bodied, floral, and smoothly-bittered. This is not what the BJCP guidelines indicate, and so I consider the BCJP wrong with regards to this style - or at least they tend to describe American-made English-style IPAs or "English Export IPAs," rather than beers called "IPA" in England. That being said, I recently brewed a beer along these lines: 4.6% ABV, pale in color (7 SRM), floral and balanced towards the hops. I just tapped it, and it's great. I say you don't really "need" English hops, just as long as you stay away from the really piney/citrusy American hops. Nugget/Willamette was a good combo for me (I even threw in a pinch of Cascade, and I don't think it made it taste any less authentic). I think a FWH addition, a 5 min addition, a flameout addition, and a light dry-hop addition is what you need (and you could probably keep out the FWH addition). I used S-04 in this last one, but I'm sure most English yeasts would be fine. I Burtonized my water, which I think is a good rule of thumb. Shoot for dry to medium-bodied (hint: not more than 10% crystal). I would give it long enough to clear, then cold crash, if you can (English beers really ought to be brilliantly clear, even if dry-hopped). Clarity is another place where choosing the right yeast can save you some time. S-04, 1098, or 1099 would be my first choices.