I haven't used Wyeast 1275, Thames Valley Ale, but I've brewed with 1056, American Ale, plenty of times, and 1056 usually isn't very clear to begin with. From the description of 1275, I doubt it would be much hazier, if any.
Given that both yeasts make cloudy beer, and that if you dry-hopped your IPA, you further muddied the waters, I wouldn't expect any less, and I wouldn't be surprised if the beer stays murky.
You can try cooling the beer to get particulate matter to drop out of suspension. I would recommend getting it down to around 40°F if that's possible with your setup.
If you're still not happy with the appearance, you can try adding finings for clarification.
Turns out, there's a great post here that covers steps to clarify beer.
Personally, I would be more interested in the flavor and aroma variations as a result of the yeast swap than any appearance changes. You should expect your beer to be less estery and taste more grainy like a British beer... should be interesting.