Hoovering and steam cleaning will keep the numbers down, but not to zero.
Transfluthrin chemical killers in your clothes boxes, drawers and wardrobes will protect the clothes, but you need a real blitz at the beginning to intensively remove and kill them. Spraying round the edges of the carpets will kill the ones hiding under the skirting boards.
When I was dealing with an infested house (not mine) I moved all the furniture to vacuum the floor thoroughly, and turned beds, rugs and sofas (they usually contain wool padding) upside down, then sprayed all round the carpets and the underneath of all the beds, sofas and armchairs, and left the room for a couple of hours with the doors and windows closed. The spray is a different chemical and will kill insects on contact. The instructions usually say keep pets and children away until it has dried. I reckon that the thorough spraying would kill all the live ones, and repeated frequent hoovering and edge spraying would catch the ones that hatched subsequently. If you have a serious infestation you should assume there are eggs everywhere, even in the airing cupboard and the cupboard under the stairs, so your initial vacuuming and spraying has to be intense. I recommend tumbling and crating or bagging all your clothes so they will be protected until you have cleared the infestation. It can take a week or so for the Transfluthrin to build up inside the wardrobes and drawers. The costs of a man's suit, or a nice dress, ruined by moths will far outweigh the cost of the mothproofers. If all your clothes and blankets are damages the cost and inconvenience is traumatic
The Transfluthrin appears to be supplied in small packages, specifically so that the tiny amount of vapour released will only protect the unventilated box, drawer or wardrobe that it is in, and will not be circulating in the room in significant amounts, so it will not kill moths or anything else in the rest of the house. The vapour breaks down in sunlight or rain, and is dispersed by ventilation.
Once you've got to grips with it, it is easy to pop a moth killer in with your winter woolies or your spare blankets when you put them away, and put one in each drawer or cupboard every few months, even when you think the problem is solved. Write the date on the moth killer so you know when it has expired. They are not smelly like old mothballs.