Britain lies on islands, so lynx can't come back itself, but must be reintroduced. Sweden is located at the same latitude and perhaps lynxes genetically should be well-fitting. Maybe it will survive for example in Scotland, or northern England, where forests and nature in general are probably better preserved. I have found in Wikipedia, that Kielder Forest is located in northern England.
In Poland lynxes were hunted not so long time ago, but new ones were coming from vast neverending forests in Belarus and Russia, like wolves. If not, lynx would extinct completely. It was also reintroduced activelly by people. Lynxes in Białowieża Forest were collared. According to some people telemetry was shortening their lives dramatically. I share these views. If not forests in the east, they would vanish because of hunting and collaring. Cats hate collars, can't live normally, hunt, copulate with such thing.