You're talking about the stuff that was discussed in Spycatcher? I believe the plan, to the extent that there was one, had Wilson being ousted in favour of Lord Mountbatten?
Okay, the only way that the UK comes out of that as anything but an international leper is if the coup is kept completely secet, and Wilson just somehow leaves office, gets replaced by an obvious right-winger, with no one wondering how that happened.
But, assuming that the world knows what happened...
"The Worldwide Anti-Communist League, representing affiliated organizations in Rhodesia, South Africa, Chile, The Miami Cuban Community, and the Unification Church, is pleased to welcome the great Christian United Kingdom to the ceaseless battle against Communist treachery."
The above letter would be the sum total of post-coup Britain's diplomatic relations. Mountbatten could have it framed and hung on his wall as compensation for losing their Security Council seat.