Kane was crowned PFA Young Player of the Year on Sunday evening after a breakout season which has seen him hit 30 goals for Spurs and score 79 seconds into his England debut.
The Tottenham academy graduate will be a known commodity for Premier League defenders heading into next season but Allen feels Kane possesses enough quality to still make an impact.
“I think that is always the question that people are going to ask,” Allen said when asked if Kane can replicate his form next year.
“Obviously, the knowledge that clubs and certainly managers and coaches will have of Harry this season means he will be the man they try to stop next year so it will be a difficult one for him.
“With the attitude and application he has shown he is a man who will score goals for the rest of his career and I’m sure he is now physically and mentally strong to deal with that.
“You have seen him come into the England squad and he dealt with that – there was a furore about him coming in because of the form he was in domestically and rightly so.
“He deserved his chance and when he has been given them he has taken them, he has had a brief taste of England and will want more – that will be the driving force in the future.”
Allen, who spent four years at White Hart Lane, scoring 49 goals in the 1986-87 season and picking up the PFA Player of the Year trophy, was part of the coaching set-up at Tottenham when Kane first joined the club’s academy.
He believes the application shown by the 21-year-old as he has moved through the ranks has enabled him to establish himself in the first team at White Hart Lane.
“It has been a meteoric rise for him this season,” added Allen. “It has been a case of perseverance, he has worked really hard. I have known him since he walked in the door at Spurs and saw the fantastic attitude he has towards improving.
“Spurs have got the dividends of that, there are a number of people at the club who need a lot of credit and for his attitude to get to where he has got to today.
“He deserves it, he has had a fantastic season and I’m sure he has a big career ahead of him. Every challenge that has been put in front of him he has faced and come through them.
“He had some loan periods that didn’t go as well as he would have liked and had injuries to deal with as well – but they have been the making of him.”