I think SA80 is the name of the whole family, whereas the individual weapons in it have various L<number> names, like L85, L86 & L22 in this case.
The MP5 was pretty widely used, especially by special forces, and had already been in service for a while at the time of the L85 & L22's adoption. Part of the idea of bullpups was indeed that they would replace both existing rifles and submachine guns, but in practice that doesn't seem to have panned out, and SMGs continued to be used.
I think SA80 is the name of the whole family, whereas the individual weapons in it have various L<number> names, like L85, L86 & L22 in this case.
The MP5 was pretty widely used, especially by special forces, and had already been in service for a while at the time of the L85 & L22's adoption. Part of the idea of bullpups was indeed that they would replace both existing rifles and submachine guns, but in practice that doesn't seem to have panned out, and SMGs continued to be used.