Yes. The NHS colour palette applies to both external and internal signage.
NHS blue and white must be used as the predominant colours for external signage because patients and the public strongly associate them with the NHS. People look for these colours when trying to identify and locate NHS services. The colour Emergency Services Red should be used for Accident and Emergency.
Internal signage should also adhere to the NHS colour palette and follow the guidelines on colour emphasis i.e. prominent use of NHS blue and white, followed by core blues and pale neutrals, moderate use of green, black and dark grey and minimal use of highlights.
For more information on the NHS colour palette view the NHS colour palette guidelines.