I accept West Ham are more popular in Romford, Ilford and the likes but there are plenty about in Chingford. You will be surprised how many people have made the 'white flight' move from East london to places like Loughton and Chingford.
I am not sure how you define heartland, but I regard it as an area where the fans are predominantly one team. Using that definition, I can't think of any area that can be regarded as a Spurs heartland. I remember when I was unfortunate enough to go to a secondary for a short period of time in Eccles, Salford. The form I was in had around 30 pupils. All the football fans were United, apart from me. What can I say, I like to stand out. When I went to the Blue Bell or the Top House in Monton, they would show every United game and the pubs were packed. Barely any City games. That for me, is evidence of a heartland. I was in Chingford with a Blue and a Newcastle fan looking for somewhere to catch a game between Spurs and Swansea. In a heartland, surely the pubs would have the game on with plenty of Spurs fans about as it was an away game. We went into a boozer and not one person reacted to the Spurs goals, yet a few cheers went up when Swansea scored. Hardly typical of what I regard as a heartland.
I have worked with police, sports clubs and local authorities (in particular, youth and leisure services) in the likes of Waltham Forest, Enfield, Barnet and Haringey. Based on my experience, not one area is a Spurs heartland. From what I have seen, there are as many Arsenal fans as Spurs fans in pretty much every area. I don't think Arsenal have a heartland either. Each have areas where a large number of fans are based.
As for Hertfordshire, I don't know if you have visited recently but from what I have witnessed, it's now very much Arsenal and Chelsea are dominant. Not sure why there are so many Chelsea fans in Hertfordshire. You only have to go to St Albans, Watford and Hertford to see how popular Chelsea are.
As to Kane, he played for a year for Arsenal U9's or something. That's almost certainly why he's wearing that shirt at that parade. I doubt that he'd lie about being a Spurs fan if he was genuinely an Arsenal fan - because every non Spurs fan he knew at that age would now be coming out of the woodwork to tell the world what a liar he is. He'd more likely just keep quiet about it altogether.
Just to make it clear, I don't think it matters but, of course, he is going to deny being an Arsenal fan. It's not wise to admit you supported a rival as fans tend to overreact to such things. Dying your hair red, wearing a shirt and attending a trophy parade looks like sound evidence to me.