I can see where the confusion may have arisen regarding the statement that " it is one institution there can only be one PI" . According to UK HRA NRES REC SOPs – Version 5.1 March 2012, section 4.7 states:- " There should only be one Principal Investigator at each site".

However later sections make it clear that if two clinical teams are working independently of each other, then the guidance says that the individual teams may be separately identified as research sites and have a PI each. What you described in your question, seems like a similar scenario where the PI "has never met or worked with" the staff of the other unit and the trial "is open across two separate clinical units".

Section 4.15 of UK HRA NRES REC SOPs – Version 5.1 March 2012: - "where the research is to be conducted in two or more entirely discrete operating units within the same NHS organisation, these units may be separately identified as research sites. Each site should have its own Principal Investigator who is accountable for the whole research team. There should be no dual accountability or overlap between research teams".
Also for GPs, section 4.16 states:- "In some cases, two or more independent practices may be conducting the research within the same health care centre. These practices should normally be identified as separate research sites".