There isn't a top three. There are only opinions.
Were I you, I'd take a day or more off and make some appointments on the Row and its near environs and do your research slowly.
Ignore the budget tailors, because you have the money. If you change your mind and decide you'd rather pay £800-2000, come back and ask again about Graham Browne, the Soho tailors, and other sub-2K bespoke.
"Reasonably structured" could mean different things to different people.
To me it means not drapey A&S things (so discount Steed/Mahon, younger Hitchcock - see the old A&S expatriates thread).
It probably means you would think that the very hard "cavalry" (my term) or "sporting"/"hacking" cuts at Huntsman, Richard Anderson and - I think - Kent, Haste and Lachter are too structured for your taste - but you have to decide. Same for whatever Dougie Hayward on Mount Street has re-invented itself as with an infusion of Kilgour cutters since Mr Hayward passed on, or Edward Sexton.
Which leaves you with the rest, really. Kilgour has history but has recently (as above) gone through some major staff changes and may well be a "harder" cut than you like (I haven't experienced any of their stuff in person for years so have no specialised knowledge). Poole is the classic - and produce a more structured look at times than you may think. But go and talk to both of them. Definitely see Andrew Ramroop at Maurice Sedwell, though I'm not sure of their pricing, which I think can be on the high side for you (and me). And definitely see Dege. Go visit Meyer and Mortimer. And the jolly chaps at Davies and Son. As Holdfast suggests, check out E and R. And, although they've focussed on RTW for 30+ years, and have just been bought by Chinese investors, even go see Gieves and Hawkes. Pop into Benson and Clegg on the arcade offf Jermyn St for a chat. And pop by all the others that I've forgotten.
If you want the traditional London bespoke experience, walk past and do not enter Oswald Boateng, Spencer Hart, Richard James and those two odd places on the West side of the Row that have novelty shirts with contrast piping and shiny silver RTW numbers in the windows.
Also go over to the London Lounge on the interwebz and do some lurking/searching. Like any internet forum, I can't vouch for the accuracy of individual posts, but you may find it useful.
However, my fundamental advice is go see everyone who might fit your bill, take your time, think about it, and then pick someone. And then let us know how it went.