I would like something in a pot here:

How about Chamaerops humilis?
The width of the wall is 100cm between the edge of the door and the corner. The tap is 70cm above the gravel. The wall faces E, and the spot gets the sun for 3-4 hours a day in summer. The wind whistles down the gap between the fence and the house, but this spot is quite sheltered. I think a sphere of leaves 30-50cm in diameter in a pot 25-30cm tall would be a good start.

Also here, to replace the yucca which is hopelessly potbound:

How about Trachycarpus fortunei?
This is the NW corner of the back garden. It’s very sheltered, and gets the sun for 3-4 hours a day in summer. The remaining yucca leaves are 140cm above the gravel. The rosa ‘Albertine’ and clematis montana are being trained up and on to the E wall of the house, so should be out of the way. A pot here could be partially buried. Access is only to the compost bins, so not critical. I think a plant 50-70cm tall from soil level to the top of the leaves might be appropriate.