Almost certainly there will have to be a planning application made for change of use for part of an otherwise residential dwelling to be used a business premises.
A further complication in terms of planning law and getting planning permission will be whether his set-up will be just for manufacturing or if it will also have a retail aspect. Unless your neighbours are very persuasive, it is far from guaranteed that such permission will be granted.
All the issues you mention about the proximity of you and other residential dwellings will be relevant when the local authority considers planning permission. I would therefore inform the local authority as soon as possible so that they can hopefully nip it in the bud and help persuade your neighbours that a blacksmith’s forge is better situated elsewhere.
In addition, while the local authority should pursue their statutory responsibilities regarding environmental and planning issues, you may wish to explore your own private law remedy by examining your land title deeds.
Within the deeds, look for clauses which set out so-called “covenants” that are intended to protect the value and character of the land by managing or restricting what can or cannot happen on it. It is common (but not universal) for covenants for residential areas to prohibit business use. The logic being business use can be disruptive to an otherwise quiet neighbourhood, or indeed impact adversely on house values.
This last point on house values is one worth picking up with your neighbours, as they may not realise letting their son attempt to use part of their premises as a forge may be detrimental to their own wealth.
Or they may be so pleased their eccentric son has found his niche that they ignore that “problem” for themselves. But as I have explained, they cannot ignore the potential problems so far as you and other neighbours are concerned.
Ask a Lawyer should not be taken as formal legal advice, but rather as a starting point for readers to undertake their own further research.