OP here. I had a fine experience with these guys, and got my cat with no trouble from UK customs/border people.
They were very responsive to all of my emails/phone calls, they charged the rate they quoted, there were some hiccups (not their fault) that they addressed admirably, my cat got here safe and sound and looking no worse for the trip.
I would recommend them highly (fairly inexpensive too . . . less than $2k for one cat from Detroit to London, which was much better than everything else I got quoted).
PS: To anyone using another pet agency, those prices are HIGHLY negotiable. . . I got one company to shave nearly $1k off their quote.