To agree with Atma-Sphere, a high damping factor amp is not necessarily the way to go with the Westminster Royal SE.
If you want to get the full bass potential of this speaker you do need the right amp. And with such a glorious, detailed, natural, open bass it is worth getting it right, believe me. I'm not a rocker or a blaster but I won't give up the great bass this speaker is capable of.
I wish the Atma-Sphere MA1 got it all but it does not in the bass. The speaker sounds light with it, and does not go down with realism in the deepest bass. I love Atma-Sphere and Ralph's dedication so this is no slam on either.
I would focus on what works for Westminster owners as that rear loaded folded horn bass presents a different load to the amp than other Tannoys. It's just a different beast.
There's a manufacturer who won't want to be quoted by name but his Westminsters sound powerful, seductive, rich, natural, dynamic, with deep bass, using a CAT amp. I heard classical, drum demo reoords, organ, rock, vocal, jazz and contrary to what an above poster says, you can get it all with one amp on the Westminsters. I am an SET triode guy with extremely efficient speakers but I would try the Westminsters after what I have heard many times at his place but I don't have the room for the Westminsters.
And, I am considering a CAT to replace my SETs. Do a search on the CAT JL2 and you will see other guys who say it sounds like the good parts of SETs but with power and bass drive.