If it’s a terraced period house it’s unlikely there is a cavity in the wall that you could fill. (Not sure about more modern terraces but suspect also unlikely). You’d need to apply some soundproofing material to your own wall. There’s lots of options, they vary in cost, effectiveness and ugliness!
You can get pre made foam or cork panels you just apply to the wall, or for a better look fit two layers of soundbloc plasterboard to the entire wall and then paint to match (but you’d also need to refit any cornice, skirting, carpet). Or would a built in wardrobe or bookcase be an option? If so that would help a lot, especially if you put soundbloc at the back of it.