Mark Sampson believes Great Britain would have added another Olympic gold to their spectacular haul if the women’s football team had avoided a political roadblock on the road to Rio.

The England manager led his team to a celebrated bronze medal at the World Cup last summer. The success would have been enough to earn any other nation an Olympic slot but the football associations of England, Wales, Scotland and Northern Ireland remain split on the question of approving men’s or women’s British teams.

Concerns that the independence of each national side might be risked meant it was only the English FA pushing for Great Britain to be represented in Brazil, when all four needed to be in agreement.

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Even before their World Cup success in Canada Sampson’s players knew their Olympic fate was sealed. The England captain, Steph Houghton, said she and her fellow Lionesses remain “very disappointed” to be absent from the Games, having played at London 2012.

Sampson said: “There’s not many people on this planet who are Olympians and this group of players did earn the right to go to an Olympics and compete and represent themselves and their country and their family and friends but it’s been taken away from them.

“I think the most frustrating thing is that not only have they not been given the opportunity to become Olympians but I’ve watched the tournament and I believe this team would have won the gold medal.”

Sweden, the team who gratefully accepted Great Britain’s spurned place, will play Germany, the side England beat in the World Cup third-place match, in Olympic final at the Maracanã. Sampson has been putting his players through their paces at a sun-baked St George’s Park training camp this week. Euro 2017 next summer will be their next big moment in the public eye.

The Olympics is inescapable, with Houghton admiring “unbelievable” performances by cyclists Jason Kenny and Laura Trott in the Rio velodrome.

Sampson said of the Olympics setback: “They’re always going to look back and think about what could have been. It would have been great to experience a tournament but it’s been taken out of our hands. All the players can do is perform in their bubble, do their best, and we’ll go next summer and work really hard to get a few more young girls thinking about football, rather than cycling or canoeing or rowing.”

Asked whether the Team GB position might change, Sampson expressed guarded optimism, albeit saying such negotiations were “way, way above my pay grade”. He added: “They’ve worked so hard for it, so hopefully something can happen that, if we were to qualify again, GB would get a chance to take part in women’s football.”

The home nations’ collective agreement to field Great Britain men’s and women’s teams four years ago may prove to be a one-off.

Houghton scored three goals at London 2012 before Great Britain, made up largely of English players, met a quarter-final exit at the hands of Canada. On Tuesday evening the 28-year-old and her England team-mates watched on television as Sweden knocked out hosts Brazil on penalties.

“That was originally our place - the place that we won at the World Cup,” Houghton said. “And it’s hard, and it’s disappointing, but at the same time it is what it is and there’s no point about complaining we can’t be there. It’s about using our energy that we could use to complain, to go into the Euros and hopefully have a great tournament over there.

“If you speak to the rest of the squad they’re very disappointed not to be in the Olympics because I think we could have gone there and done really, really well.”