In the days before John Fashanu, Viv Anderson and Ian Wright came along, much the same falsehood was perpetuated about black footballers - along with the one about not playing well in the winter, which is also thrown at foreign players.
The slurs are as inaccurate when applied to players from abroad as they were about black ones. Sure, we can all think of players who are inclined to go missing when the footballing temperature rises, or climactic one drops, but they are just as likely to be white and British.
Yet the myth persists, even in defeat. On Saturday, Aston Villa came to Stamford Bridge to stop Chelsea playing and, though they did not set out to kick them off their game, nor were Villa's all-British XI going to tread softly.
"You have got to get in their boots," said John Gregory, the Villa manager, after a defeat which was more comprehensive than the 1-0 scoreline suggests. "You have to get contact with your opponents."
Gregory, it should be made clear, was talking about being physical within the laws. As he added: "They were the best footballing side we played last year and, like the clubs we played pre-season, Ajax, Fiorentina and Feyenoord, if you give the ball away you don't get it back for 10 minutes. You cannot stand off and let them play around you."
There were a few hefty challenges, notably from Alan Thompson on Dennis Wise, but Chelsea were neither rattled nor riled. And it is the latter which is more of a danger. Wise, Sutton, another Englishman in Jody Morris, and foreign players like Marcel Desailly and Gustavo Poyet know how to look after themselves. They did incur three bookings, making it 10 in four games, but, helped by the strict refereeing of Neale Barry, kept their heads.
Instead they concentrated on their passing and, despite Villa's attentions, regularly did pass the ball around their opponents. Morris, enjoying a rare outing, justified his place as did Villa's Mark Delaney, who arrived from Carmarthen via Cardiff for pounds 300,000. Proof that bargains can be found this side of the Channel. This comment, and the wish that Morris gets a run (unlikely as Didier Deschamps should be fit to play in the Champions' League qualifier in Riga on Wednesday) are not xenophobic - foreign players are good for the English game, but not in excess.
If the theory that Chelsea are a soft touch is mistaken, the belief that their finishing is poor is not. Chances were missed against Sunderland, Skonto Riga and Leicester and it was the same on Saturday. Dan Petrescu twice chipped over with only David James to beat, Gianfranco Zola sent a clear header too close to James and Poyet put another one wide. In addition, several half-chances came and went while the goal that was scored needed a helpful toe from Ugo Ehiogu to steer Petrescu's shot inside the far post. It was justice of sorts, Ehiogu having escaped a first-half penalty for tripping Zola.
Wayward finishing was one of the three reasons Chelsea failed to win the title last year. The others - apart from the fine form of Manchester United and Arsenal - were the absence of Poyet and their inability to hold a lead under late bombardment.
Poyet is back, his injury problems gone if not forgotten (he will not do interviews because, he says, every time he does he gets injured). His value was underlined by Villa detailing Ian Taylor to man-mark him.
Equally importantly, the defence is beginning to stiffen. It faltered without Marcel Desailly at Filbert Street last week but this time it withstood Villa with relative ease.
"We defended with composure but kicked it away when we needed to," said Gianluca Vialli, the Chelsea manager. "It was very satisfying because [Dion] Dublin is strong and [Julian] Joachim is quick. We showed solidity"
And what was his response to Savage's "Dad's Army" philosophy? "It is good to be criticised, it makes you think and get better. Too much praise and you might think `I'm too good and then not work hard'." The gap in quality was dispiriting for Villa but Gareth Southgate found recompense in the improvement since last season when he admitted: "They pulverised us. This time," he added, "we had more of the game and we did cause them some problems, which we didn't do to teams like Chelsea, Arsenal and Manchester United last year."
So will it be the same three again this year? "Not necessarily," insisted Gregory. "This could be the year someone comes from the pack and not just because of Champions' League commitments. A lot of teams have strengthened this year. Today I could look at my bench and I had players who could change things." He also had George Boateng, Steve Watson and Najwan Ghrayib unable even to make the 16. However, Villa - who only tested Chelsea once with a 34th- minute Ehiogu header - do not appear to have enough on the pitch to worry the likes of Chelsea when the season's judgement day arrives.
Goal: Ehiogu (og 52) 1-0.
Chelsea (4-4-2): De Goey; Ferrer, Desailly, Lebouef, Babayaro; Petrescu (Goldbaek, 76), Morris, Wise, Poyet; Zola (Ambrosetti, 87), Flo (Sutton, 76). Substitutes not used: Hogh, Cudicini (gk).
Aston Villa (3-5-2): James; Ehiogu, Southgate, Calderwood (Stone, 76; Draper, 88); Delaney, Taylor, Hendrie, Thompson (Merson, 70), Wright; Joachim, Dublin.
Substitues not used: Barry, Oakes (gk).
Referee: N Barry (Scunthorpe).
Bookings: Chelsea: Poyet, Sutton, Lebouef. Villa: Taylor, Hendrie, Thompson.
Man of the match: Zola.