At the Emirates on Sunday just after 4pm Alexis Sanchez floated in a high-pressure last-gasp penalty kick, for his 15th Premier League goal of the season, to secure the win that took Arsenal to second.

At Stamford Bridge soon after 5pm Diego Costa stroked the ball into the bottom corner, for his own 15th league goal, to set up the win that kept Chelsea eight points clear of Arsenal at the top. Any questions about his inclusion had been wholly answered.

It was another afternoon which showed just how indebted England’s best teams are to these South American strikers. Liverpool, of course, have Roberto Firmino, who scored his seventh and eighth league goals on Saturday, with Philippe Coutinho in support. Manchester City have Sergio Aguero (11 league goals) and now Gabriel Jesus too.

Diego Costa shakes hands with Antonio Conte after being replaced against Hull (Getty Images)

And yet as Arsenal and Chelsea know desperately well by now, they cannot secure the futures of these two indispensable men. Sanchez has 18 months remaining on his Arsenal contract and he has been offered a £25million salary by Hebei China Fortune. Arsenal have found negotiating a new deal for him desperately hard and they will have to break their own wage structure to get anywhere near what Sanchez wants. Wenger is asked about this at his press conference every week but can never give new answers.

The Diego Costa saga has not been running for quite as long but the outline is the same. He has one more year on his contract than Sanchez, taking him to June 2019 not 2018. But he has a £30m salary offer from Tianjin Quanjian and, quite understandably, he wants to take it up. Chelsea will not offer him anything like that but by this summer they will likely either let him go to China, back to Atletico Madrid, or try to keep him with a generous pay-rise.

It is very plausible that for both Costa and Sanchez, this will be their third and final season in England. It would be a desperate shame for the Premier League to lose its two most effective attacking players. If they go they will not be replaced by players nearly as good.

Sanchez converted from the spot deep into stoppage time for Arsenal (Getty)

But this is the dilemma that English football has been in for the last 10 years or so, ever since it became so reliant on importing its strikers from South America, because Europe does not produce them anymore. All of the best strikers in England, certainly since Cristiano Ronaldo left for Real Madrid, have come from South America, growing up in a far more competitive, far less structured environment. At least one of Carlos Tevez, Aguero and Luis Suarez has been in the top three goal-scorers every season since 2009-10. A plush academy is not as good an education as the street.

Tevez and Suarez achieved great things in English football, Tevez winning the title with both Manchester clubs, Suarez nearly winning the 2014 title for Liverpool single-handedly. But for both players their time here was dominated by their own obvious discomfort at living and playing in England. Tevez had his five-month strike during the 2011-12 season, Suarez repeatedly agitated for moves before joining Barcelona in 2014.

Carlos Tevez shone in England too, but couldn't wait to leave (Getty Images)

Costa and Sanchez could be as effective as Tevez and Suarez but we must not kid ourselves that they are in England for the long-haul. They are a long way from home here and while their big Home Counties houses must be comfortable that does not mean the same as comforting. If they are offered four or five times their salary to go and play in a country that is not four or five times more alien then it is not as strange a decision as has been made out.