Lobbying from interested parties. In this case, the Classic Car enthusiasts. The government most likely judged that allowing a dispensation for commercial sale would not in fact result in widespread continued use of leaded fuel due to the commercial realities of selling such a niche product, but it was worth the effort to say they supported this niche - and that's exactly how it turned out.
The original 1999 UK legislation envisions retailers will be given a maximum quota on how much leaded they can sell, a permit holder could sell 0.5% of volume per month for example. But as anticipated ordinary motorists just put unleaded in the tank and carried on as before so the quota system was pointless. If your "quota" is 10 000 litres of leaded fuel per month and you sold a total of 45 litres to one bloke in that time, you not only don't need a bigger quota, you won't order any more of that fuel from your supplier. If perhaps, the next summer, a motorist in a Victorian outfit driving a 1926 Chevrolet enquires about the leaded fuel you tell them "Sorry mate, we're out of stock" and most likely they put unleaded in the tank, but either way they're not wasting your time and money with this weird "leaded" fuel nobody buys.
Which is why there was an archive.org link above -- the actual site for the FBHVC now tells you that you probably can't get leaded fuel, and even if you could you shouldn't bother, even though that's the organisation identified in the legislation itself as asking for this exception.
I assume it's still technically legal for whoever actually bothered to have a permit - but the actual emissions involved must be pretty tiny.