JCT Standard Building Contract 2009 and JCT Design and Build Contract clause 3.2 explicitly stipulate that a person-in-charge must be on site “at all times”. However, the expression ‘at all times’ is not to be interpreted literally, so should the person-in-charge be off site for a trivial period of time it would not be considered reasonable to halt work.
That said, under JCT Standard Building Contract 2009 clause 3.15, JCT Design and Build Contract clause 3.10 and JCT Intermediate Building Contract 2009 and JCT Intermediate Building Contract with Contractor’s Design 2009 clause 3.12, architects are explicitly granted the power to postpone any work if there is no suitable person-in-charge, so in principle the answer to this question is ‘yes’.