Gareth Southgate’s side booked their place at the finals in Russia with a lacklustre 1-0 win over Slovenia at Wembley on Thursday.
England’s wretched display somehow ended on an upbeat note when Kane stretched to convert Kyle Walker’s cross in stoppage-time.
The Tottenham striker, named England captain for the night, was one of the few players to emerge with any credit as he continued his hot streak.
Kane has followed up successive Premier League golden boots with a blistering run of 14 goals in nine games for club and country.
He has now struck 11 times in 22 appearances for his country and looks one of the only genuine world class talents available to Southgate.
But Kane is adamant England have enough quality in other positions to help him shoulder the burden in Russia.
“It isn’t down to just me, it’s down to the whole team,” Kane said.
“We’ve all got to work together as a unit. I feel physically great, every game I expect to score so I have to keep it going.
“When you’ve got someone scoring goals it helps and hopefully I can continue that from now until then, we’ll see what happens.
“But I don’t want to get too far ahead of myself personally and I don’t want the team to get too far ahead of themselves.
“I just have to keep doing what I’m doing for club and for country and see what happens next year. We can’t put any limit on what we can achieve, we just have to go there and see what happens.”
England defender Gary Cahill was relieved to see Kane’s latest display of predatory finishing put a flattering gloss on his team’s spluttering display.
– ‘Gushing with confidence’ –
But the Chelsea star agrees with Kane that England must get quality contributions from other areas for Southgate’s men to have any chance of making a sustained run in Russia.
“He’s in great form and he must be gushing with confidence,” Cahill said.
“He must feel like he’s going to score every time he takes the pitch. Not even one, it’s like ‘how many am I going to get today?’ He must have that kind of mentality.
“But every good team has people who contribute all over the pitch. He’s been fantastic for us but you don’t want to go into a tournament with everything on Harry Kane.
“We want him to be in fantastic form but we want everyone to contribute. Going into the tournament we want everyone to have the kind of confidence he’s showing at the minute.
“The fearless mentality — that’s the way he is at the minute.”
After dismal early exits from Euro 2016 and the World Cup three years ago, there is little expectation that England will do better this time.
Even their fans seem to have given up after they spent most of the Slovenia qualifier entertaining themselves by throwing paper aeroplanes onto the pitch.
“From the fans’ perspective, if you look at the last time we won anything for England it was a long, long time. So naturally they don’t expect. But I’d like to think everyone is positive and behind us,” Cahill said.
“I think to go into the latter stages would be looked on as a success if I’m being honest.”