And correctly so, in my opinion.
Since UK law does not impose its prohibitions / severe restrictions on "handguns", but rather on "short firearms" (those with barrels under 12". and / or with an overall length under 24"), the so-called LBR's and LBP's, as you correctly said, have no legal classification as a category unto themselves.
Legally, they are NOT "short firearms". Therefore, they are "rifles", and should be subject to the same restrictions as other cartridge rifles: no more and no less.
It's the police, not the law, who have (incorrectly) decided that this type of rifle should be more severely restricted than other types.
Jim