You will be able to see if they own out to the centre of the road if you obtain a copy of their land registry map. If their house is in an estate, and yours is in the same estate, you could in the first instance have a look at your own map and see what the situation is with your own house as this will give an indication. It will also help you to pinpoint where their property is when trying to get a copy of their map. If it is registry of deeds it is unlikely you will be able to establish this as you will not be able to obtain a copy of their map.
Again if it is an estate, the planning for the entire estate may contain conditions in relation to the location of their front wall. If not, planning for a once off house may also contain a condition as to the location of the front wall viz a vis the roadway- so if they change the location of the wall they could be in breach of planning. So you could also obtain a copy of their planning permission from your local planning authority.
Otherwise generally I believe you are correct in stating that a wall below a certain height does not generally require planning- however I'm not an expert on planning.