A relative has lean-to roof.
Concrete marley etermit tiles on batons, felt, T&G close-boarded,
rafters. 22-degrees.
Close-boards stop at the double-brick wall, tiles are then bedded on
felt, on mortar, with mortar edging.

Over the double-brick wall at a north-facing corner for about the
bottom 15" the mortar is falling out and the felt is disintegrating.
Interesting population of woodlice. The result is a damp stained
plaster-skim over browning for about 6-inch below and a plywood
cupboard has delaminated rather spectacularly over about 3-inches. It
is a kitchen below so damp loves company on a north facing wall re dew
point. Ventilation is now 220+270m3/hr, open gas appliance removed.

Q - How can I effect a reliable roof repair?

Is it a case of wedge & lift tiles, put impermeable membrane over the
wall on mortar, bed the tiles back on mortar.
What is the best membrane to use - felt rolls are too heavy for me to
handle.

At some point the roof needs redoing with more appropriate low-angle
interlocking tiles, I'm unsure if the ceiling fixed to rafters makes
that more difficult, but in any case putting the job off a while would
be useful since it will be me that has to subsidise. The other side
appears ok, at least relatively speaking.