Not true.  While the role of the fire and rescue service does, by definition, involve rescue, this should be a last resort when safe evacuation without external assistance has failed. In all buildings other than those with a stay put policy, the responsible person is responsible for the setting up of a fire evacuation procedure and fire precautions that enable this procedure to be carried out in a reasonable and timely fashion, with persons, such as fire wardens, to assist with evacuation.  Many buildings are equipped with fire refuge points (at the tops of stairs for example).  These are for disabled persons to be taken from (using whatever equipment or personnel are necessary), not to be abandoned in for rescue by the fire and rescue service.

In the case of premises with stay put policies (such as purpose built blocks of flats with good compartmentation etc), evidence suggests that fire and rescue services are summoned and arrive in time to avoid wide-scale evacuation of residents (except those in the flat where the fire starts).  If evacuation beyond the flat in which the fire starts is necessary, residents will be notified of the need to evacuate by the fire and rescue service.