There was a great deal of, at the time, VERY quiet cooperation by the U.S. & NATO with the UK.
It was both more and less simple than that...
There were really 3 types of cooperation.
First, the visible stuff, help in negotiations, things like replenishing the NATO war stocks the British were using (things like the latest mark sidewinder, for example)
Second, the things they were keeping reasonable secret, to avoid any embarresment - things like the satellite data, other intelligence, the fact that US planes were actually airlifting supplies direct to Ascention - nothing illegal, but they didnt want it too widely known.
The third was the one that got very little attention at the time (unless you were involved with people doing it

, which was all the face to face and phone calls going on between British officers and their US equivalents. Remember, these guys had trained in NATO together for years, knew each otherw ell -and after all, a phone call isnt official policy, right?

But a surprising amount of stuff was arranged that way.
And of course, the press made a big fuss of some of the public (and not necessarily that important) help while a lot of the really helpful stuff was kept very quiet indeed.