I am pretty confident in saying that more UK golfers will know of Pete Dye than of the likes of Donald Ross, Tilinghast, Hugh Allison, Herbert Fowler, Tom Simpson, Raynor or C.B. Macdonald. Only really Mackenzie, Colt, Braid, Old Tom and a few other local architects (Tom Williamson in the midlands for example) are known to most golfers in the UK. Most don't know or care who designed their course. I'd be confident in betting that 80-90% of the members of the course I grew up and only recently left wouldn't know who designed the course they play on today.
Pete Dye's name whether involved or not will be a great draw, mainly for his work at Sawgrass which is probably as famous over here as any major venue in the US bar Augusta. And as Adam has stated the Menai-Davis family run a successful golf course business at The Shire so will no doubt know how to get the most from the new course. Being in Egdware it will even be accessible in theory via the tube so the potential catchment area is huge. I'd be hugely surprised if it wasn't a success.