No it can't. A horsebox is neither a van nor a lorry, regardless of size.
You're talking rubbish. A lorry is a lorry. The body type makes it a van, flat, curtainsider, livestock carrier, horsebox or whatever.
At 7.5tn, it wouldn't have been a lorry. It would be a large box van. 7.5tn vehicles can be driven on a normal car licence (if you passed before 1997). Vans can be driven on a car licence, lorries cannot.
Aren't you full of rubbish? Have you listened to yourself. Your imaginary definition of 'van' is therefore that it can be driven by someone who, if they'd passed their car test 31 years ago, would have been able to drive it without a further qualification?
So you're basing you definition of vehicle type on an arbitrary qualification which became obselete 31 years ago, rather than the actual vehicle type which we can see with our eyes?
It's a mystery why you're even bothering to argue the point anyway but why on earth are you tying yourself in such knots asserting that black is white when it doesn't even matter?