World Cup winner Lewis Moody hopes England do not claim the Grand Slam now as it could see them peak too soon.
The 23-13 result against France on Saturday
means Stuart Lancaster's side are just two games away from a clean-sweep in this year's Six Nations.
With the next World Cup coming in 2015, Moody, 34, is concerned the achievement could hamper England's long-term hopes.
"Part of me wants them not to win it because you have to maintain that level of high performance," he told the BBC.
England's Six Nations fixtures
- 2 February:
England 38-18 Scotland
- 10 February:
Ireland 6-12 England
- 23 February:
England 23-13 France
- 10 March:
England v Italy
- 16 March:
Wales v England
"Winning the Six Nations is very important this year, they will do that, but the Grand Slam... We will see, but the team is moving in the right direction."
England - with the now retired Moody often playing an impact role as a replacement flanker -
last took the Grand Slam in 2003 with an emphatic 42-6 win against Ireland,
following several painful near-misses in previous campaigns.
Importantly, that victory came just eight months before
the lifting of the World Cup in Australia thanks to a dramatic extra time drop-goal from Jonny Wilkinson against the hosts.
If the current players are to repeat that Grand Slam-winning feat, they have a much longer wait to try and follow that with a World Cup triumph, which would come on home soil.
Italy are the next visitors to Twickenham in a fortnight's time, with England's campaign ending in mouth-watering fashion a week later in Cardiff's Millennium Stadium against the reigning champions.
"It was not a massively impressive performance against France, it was just a really good win,"
former England captain Moody said.
"Sometimes you just have to win and beat the team put out in front of you and at the weekend that happened.
Lewis Moody at a glance
12 June 1978
- Club record:
Became the then youngest player to feature in a senior game for Leicester in a 16-year top flight career that finished while with Bath in 2012
- International career:
Scored nine tries in 71 appearances for England, a nation he also captained
- Club honours:
Won seven Premiership titles with Leicester as well as two Heineken Cups
- International honours:
Featured in all seven matches as England won the World Cup in 2003, a year in which he also helped claim the Six Nations Grand Slam
"England re-grouped in the second half and showed some really intelligent play, there was a lot of coolness under pressure. They have the three wins back-to-back and they will beat Italy.
"It is then a big ask to win in Wales."
On a freezing day in west London which saw England battle back from a half-time deficit fly-half Owen Farrell continued his impressive form with the boot by adding 12 points, though he also twice got involved in physical confrontations with France full-back Yoann Huget.
has been told to rein in his spiky nature by World Cup-winning head coach Sir Clive Woodward,
but Moody chose to praise the aggression.
He said: "I like to see that my fly-half has a bit of passion about him. Owen is so consistent and he is a great performer, he has shown that with his kicking.
"But there are going to be times in a game when your emotions and passion to win is sometimes overtaken by your natural instincts. Owen is only a young man and that is bound to happen."