Update by Simon Braun:
In my last update, I mentioned the possibility of enforcing possession orders by obtaining Injunctive relief, which is specifically excluded from Practice Direction 51Z prohibiting enforcement of possession orders during the current pandemic. I can now report that Mr Justice Chamberlain recently made such an Injunction Order. The case is University College University Hospitals NHS Foundation Trust v MB. MB was occupying a bedroom in the Hospital which she no longer needed but refused to leave the Hospital. The Hospital claimed possession of the bedroom and upon the Judge pointing out the limitations due to PD51Z, the Hospital amended its claim to seek an Injunction requiring MB to leave the bedroom.
The Judge granted the Injunction which required MB to leave the Hospital and not to obstruct or impede the transfer arrangements made by the Hospital for MB. I suspect it was argued that the case was urgent given the lack of capacity in hospitals during the current crisis, which would have no doubt swayed the Judge in his decision to make a mandatory Injunction Order. However, it does appear to be clear that in urgent cases, possession will be able to be obtained notwithstanding the current prohibition to enforce possession orders.