Eddie Jones has taunted Warren Gatland after the Wales coach questioned whether England have played their World Cup final a game early by overwhelming New Zealand.

Gatland was speaking after his team had been beaten 19-16 by South Africa, who now face the 2003 champions on Saturday in a repeat of the 2007 showpiece.

Twenty four hours before England and the Springboks collide at International Stadium Yokohama, Wales will confront the All Blacks in the bronze final 24 hours earlier – Gatland’s last match at the helm.

“Well, guys, can you just send my best wishes to Warren to make sure he enjoys the third and fourth place play-off,” Jones said at a press conference on Monday

Jones and Gatland are long-standing sparring partners and the outgoing Wales boss on Saturday made a pointed remark about England’s crushing win against the world champions.

“We have seen in previous World Cups that teams sometimes play their final in semi-finals and don’t always turn up for a final,” Gatland said.

“So it will be interesting to see how England are next week and it could be a good game.”

Jones has seen off heavyweight rival coaches Gatland, Steve Hansen and Michael Cheika so far in Japan, but he has even grander aims as the UK staggers through its Brexit ordeal.

If South Africa can be overcome, he hopes it will lift the gloom of the nation.

“It’s great – you give the country something to cheer about and with Brexit at the moment they probably need something to cheer about,” Jones said.

“It’s the job of a team to make the country happy and we’ve made the country happy. Not as happy as they can be because there is still a game to go as we’ve said.

“The crowds here generally in the World Cup have been fantastic and I thought our supporters on Saturday night were massively instrumental in helping us get home.

“Their singing and their general support of the team has been outstanding. We urge them to keep doing that.”

Jones has delivered a major boost to hopes of winning a second World Cup by declaring Jonny May has recovered well from the dead leg sustained in the 19-7 rout of New Zealand.

The Leicester try machine was touch and go to face the All Blacks because of a hamstring issue and, having recovered from that, he lasted 45 minutes before suffering an additional injury setback.

“We had a walk through this (Monday) morning and we had to tell Jonny to slow down a bit,” Jones said.

“He’s probably in better condition than he was last week at this stage. Immeasurably better.”

Owen Farrell also incurred a dead leg in the first-half of arguably the greatest victory in English rugby history but he managed to finish the match, albeit while handing the kicking duties to George Ford.

“Owen’s a bit sore but he’ll be fine. We’ve got a few others carrying bumps and bruises because it was a tough old game,” Jones said.

England will on Monday be joined at their Tokyo base by Ben Spencer, the Saracens scrum-half who has been summoned as an injury replacement for hamstring-injury victim Willi Heinz.

Heinz’s tournament is over but he will remain with the squad to help prepare Spencer, who will make his World Cup debut as a replacement in the final.

“It’s tough for Willi. He’s been a great contributor, a very well-liked member of the squad, and he was in tears in the dressing room,” Jones said.

“It’s tough for him but he’s now collected himself and he knows he’s got another role to play for us and he’ll fulfil that role really well this week.

“The great thing is Willi wanted to stay and we wanted him to stay so it wasn’t a hard discussion. He’s just a great bloke. He works hard for the team.

“It’s like when you want to get married. If the lady wants to marry you and you offer to marry, it’s a pretty easy conversation. So it was an easy conversation.

“Ben Youngs and him have got a really good relationship and even now he’s already started to mentor Ben Spencer. He’s a really great team man.”