Ivy is “well-known” for damaging walls.

It is very common for ivy to grow on historic walls and there is much speculation about the damage it may or may not be causing. […] This report describes research commissioned by English Heritage (now Historic England) […] undertaken by the School of Geography and the Environment, University of Oxford.

Conclusion:

Roots damage stone, mortars, pointing: Depends on whether there are pre-existing defects in the wall – ivy can exploit defects not create them

Ivy is an effective microclimate buffer, reducing extremes of temperature and relative humidity. It also buffers against damaging frosts and filters airborne particulates.