What are the regulations around fire-safe doors?
The following government guidance details the requirement for fire doors (DCLG fire safety guide for residential care). It can be downloaded at https://www.gov.uk/government/publications/fire-safety-risk-assessment-residential-care-premises
When carrying out a fire risk assessment, the full guidance contained within the document must be considered, but in relation to the question being asked, Appendix B provides technical information on fire-resisting separation, fire doors and door fastenings.
In addition, it is Article 17(1) of the regulatory Reform (Fire Safety) Order 2005 that requires the responsible person to ensure that all fire doors are correctly installed and adequately maintained.