Roofer will say it needs felting, he wants the work! House of that era is unlikely to have cavity walls, 9" solid brickwork is the norm.
I'd say the gutter is overflowing, and the water is pouring over the edge, then running down the wall and finding its way inside. Probably best solution is to get a downpipe added on your property, so hopefully it'll keep your section of gutter draining correctly. It can be difficult to align a gutter to fall correctly on these old properties as you're governed by the corbelling in the brickwork.
I'd say the gutter is overflowing, and the water is pouring over the edge, then running down the wall and finding its way inside. Probably best solution is to get a downpipe added on your property, so hopefully it'll keep your section of gutter draining correctly. It can be difficult to align a gutter to fall correctly on these old properties as you're governed by the corbelling in the brickwork.