Hi Lucy
Claimants can be awarded mobility even if they are housebound.
It's only on the question planning and following a journey that where a claimant never goes out because of overwhelming psychological distress, they cannot be awarded points for 1f, and would be awarded points for 1e. The explanation is on page 81 of the Guide to PIP Claims and Reviews.
BIS
Nothing on this board constitutes legal advice - always consult a professional about specific problems