On 7 October, the nation will go into next year's draw in company with the rest of the 16-strong elite - Australia, Austria, the United States, Russia, France, Belgium, Brazil, Czech Republic, Germany, Italy, Slovak Republic, Spain, Switzerland, Zimbabwe and Ecuador or the Netherlands - rather than be left behind to scuffle in zonal competition.
The first round is due to be played in the first week of February, immediately after the Australian Open, by which time Henman and Greg Rusedski may have rediscovered the sparkle that took them into the world's top 10. As Henman said: "Your form is temporary, and hopefully your class is permanent."
Take away Henman and Rusedski, and Britain have no class players whatsoever, which was why both men, after celebrating the success, reminded the Lawn Tennis Association again of the urgent need for reinforcements.
"We need some younger players to come up and help us," said Rusedski, who completed an entertaining tie, watched by a capacity 10,100 spectators on each of the three days at the National Indoor Arena, by defeating Grant Stafford, ranked No 500, in the "dead" rubber, 6-4, 7-5, to give Britain a 4-1 winning margin.
"There's only two of us in singles, and if one of us gets injured we're really struggling," he said. "We need to find an extra singles player and a doubles team. To play three best-of-five-sets matches on three consecutive days is difficult."
That was Henman's workload over the weekend. He won his opening singles rubber against Grant Stafford on Friday, to give Britain a 2-0 lead, and partnered Neil Broad in Saturday's doubles, a 6-3, 7-6, 6-4 defeat by the superior teamwork of David Adams and John-Laffnie de Jager.
Fortunately, Henman still had the wherewithal to mask the flaws in his game and out-play Godwin, who rose above his world ranking, 198, and tried impressively to mark his Davis Cup debut with the win of his career.
While not possessing Henman's finesse, particularly at the net, Godwin was prepared to attack his opponent's loose serves and hope that the world No 7 would fail to make the most of his opportunities to break. He was disappointed. Henman produced successive aces to save two break points in the second game and began to assert himself after breaking to love for 3-2. Henman broke again for 5-2. There seemed little prospect of a contest after Henman swept to a 5-0 lead in the second set. He then lost 10 of the next 12 points before recovering to secure a two-sets-to-love lead after 72 minutes.
Godwin survived from 0-40 in the opening game of the third set, after Henman hit a glorious backhand pass down the line, and Henman contributed the second of two extraordinary service games, a mixture of aces and faults, before breaking for 2-1, saving two break points, and cracking Godwin decisively for 4-1.
"Tim today got a lot of his timing back," David Lloyd, British captain, said. "He made a lot of difficult shots look very easy." Henman found the weekend "very satisfying, because it was by no means going to be an easy match, and I came out and did a professional job''.
The two Britons have a contrasting schedule this week. Rusedski is going to the $6m Grand Slam Cup in Munich, where he is drawn to play the Brazilian Gustavo Kuerten in the first round tomorrow night. "I've had about 10 sessions of treatment [on a groin strain] between Friday's singles match and today's," Rusedski said, "and I feel I'm moving well, serving well, and hitting the ball well."
Henman is going to France for the ATP Tour event in Toulouse. It was there, many years ago, that Jimmy Connors was asked, "Do you like playing Toulouse?'' "Of course not," Connors said. "I like playing to win."