I think the natural habitat of wild boar in the UK would see a net benefit from their re-establishment, for reasons already explained by other posters.
Sabre tooth cats and mammoths would pose no danger whatsover to the rest of the ecosystem. It is them who would be in peril, which is why they aren't here now.A bit more extreme an example would be could the Earth as we know it survive re-introduction of sabre tooth cats? Mammoths? Dinosaurs? After all, they were all once "native" species.
Dinosaurs would have even more trouble. Their immune systems would be 65 million years out of date and their biology would be adapted to a world with a significantly shorter day length. T. rex, which was a scavenger, would starve to death quite quickly unless there was a decent supply of giant vegetarian dinosaurs, and there simply isn't enough vegetation on the Earth at the moment to sustain a population of giant vegetarian dinosaurs.
Also...when we talk about "native British species" we are specifically referring to the flora and fauna which re-populated these islands after they were covered with an ice sheet which obliterated everything in its paths. The ecosystem of the UK started almost from scratch 10,000 years ago. Anything that was here before the ice came cannot be considered native.