Eddie Jones has hit back at Warren Gatland after the Wales head coach had suggested England have peaked too early in their pursuit of the World Cup, telling his old sparring partner to “enjoy the third-fourth place play-off”.

Jones also insisted that it was his players’ job to “make the country happy” amid ongoing Brexit strife back home and delivered a positive injury bulletin as England set about preparing for the first World Cup final for 12 years on Monday.

Eddie Jones and gurus relish finest hour in their pursuit of perfection | Robert Kitson Read more

Twenty-four hours after England demolished the All Blacks to install themselves as the world’s No 1-ranked side and favourites for the World Cup, Wales were edged out by South Africa and will face New Zealand in the bronze medal match, a day before the final, in what will be Gatland’s last match of his tenure.

After their semi-final defeat Gatland praised England’s performance but questioned whether Jones’s side would be able to repeat the same levels of intensity a week later against the Springboks. “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.”

The two coaches have often clashed over the last few years and when Gatland’s comment was put to Jones, he replied: “Well guys, can you just send my best wishes to Warren and make sure he enjoys the third-fourth place play-off.

Jones added: “We played a great team on Saturday but we don’t feel we’ve played as well as we can and the challenge for us is to keep improving. And there’s small margins now. As you go through the tournament, the margins get smaller. The improvements you can make are still significant – we’re looking to see how we can keep improving for this week’s game and that’s the exciting part for us.’

With England seeking the second World Cup title in their history on Saturday, Jones has also been boosted with Owen Farrell, Jonny May and Kyle Sinckler all passed fit to face the Springboks. Farrell and May suffered dead legs against the All Blacks while Sinckler hobbled off early in the second half. “[Jonny May is] pretty good. We had a walk through this morning and we had to tell Jonny to slow down a bit,” said Jones. “He is probably in better condition that he was last week [when he had a hamstring injury] at this stage. Immeasurably better. Owen is a bit sore but he will be fine. We have got a few others carrying bumps and bruises because it was a tough old game.”

Facebook Twitter Pinterest England captain Owen Farrell is on course to make the final against South Africa. Photograph: David Rogers/Getty Images

Meanwhile, amid reports of ticket prices for the final soaring to more than £12,000 and a surge in demand for flights from the UK to Japan, Jones saluted his side’s supporters and acknowledged England were giving fans a welcome distraction amid political chaos back in the UK. “I think it’s great, you give the country something to cheer about and with Brexit at the moment they probably need something to cheer about,” said Jones. “It’s a job of the team to make the country happy, not as happy as they can be, because there is still a game to go. The crowds here generally at the World Cup have been fantastic and I thought our supporters on Saturday night were massively instrumental in getting us home. Their singing, their general support of the team were fantastic and we urge them to keep doing that.”

Eddie Jones tells England to find another level to win Rugby World Cup | Gerard Meagher Read more

England were on Monday still waiting to hear whether they would be fined for their V-shaped response to New Zealand’s haka before their semi-final victory. England’s players revealed that Jones was behind the plan to counter New Zealand’s traditional Maori challenge in order to show they were “ready for anything” and it had the desired effect with Manu Tuilagi opening the scoring after just 96 seconds.

It is understood that England breached World Rugby’s “cultural ritual protocol” however, with players crossing the halfway line while the haka was performed. In 2011 France formed an arrow shape and advanced on New Zealand while they performed the haka before the World Cup final and were subsequently fined £2,500 for a similar breach. It is believed World Rugby were due to discuss the matter on Monday but the governing body’s position is complicated by the fact that it posted an official video of the incident on YouTube, entitled, “England’s incredible response to intense New Zealand haka.”