So, I seem to have had some success (after two months of seeing around 6 a day, I'm now seeing about 4 a week).
Tools (my rating out of 5)
5. Sticky pheromone traps - make sure to get them designed specifically for carpet moths. Put two traps in each room & replace with a new one after a couple of months or if the stickyness is reduced. Be very careful not to step on them or flip them over because that will ruin their stickyness.
4. Small handheld wireless vacuum cleaner - it is difficult to kill the moths, especially when they are on a wall, without making a huge mess of your walls. The moths are quite delicate and make a dirty mark when squashed. The moths don't fly away quickly either so it is really easy to catch them like this. Even when they are flying, I have found this to be the most effective means of getting rid of them. When you see one new one, look out for more as there could be a new hatching or possibly the conditions are right for mating.
3. Isolate outbreak! - close the windows and doors to the room so they don't spread to other rooms. Apparently they stay close to where the lava is and breed there so it is quite feasible to keep them contained. Keeping your windows shut will stop them going through one of your windows and into another room that way. Also, I believe the pheromone traps could help attract new moths from outside but I guess they should just get stuck to the trap so maybe not so much of a concern.
3. Vacuum the room often and thoroughly with a powerful vacuum I vacuum once every two weeks normally but, it takes a while. I think this is very effective but I give it a 3 because it is time consuming and a good powerful vacuum costs about £300 however in terms of effectiveness this is good. I did consider one of the automated vacuum cleaners but I have a lot of stairs where they are not very effective.
2. Mark location of sightings - to make it easier to know where to look next time. I use post it notes on the wall. It helped me work out where to keep an eye out.
1. Fly swatter - sometimes you see them flying around. I bought a pack of 10 for £10 and left one in every room, in the hallways etc. When flying they are really difficult to hit and I found the vacuum cleaner more effective, although when you're relaxing of an evening it is nicer just to not run upstairs to get the vacuum cleaner!
0. Bug spray - I sprayed one room a lot. It didn't get rid of them, it may have lessened the numbers but seemed to affect my skin and my breathing when in that room for a couple of weeks afterwards. If you need to use that room, have asthma, pets or children I don't think this is a good option.
Good luck, I do think it may be a few more months before I'm completely rid of them and quite possibly I will always have to keep an eye open (apparently the neighbours have them and they are a particular problem in my city so new seeds for infestation could quite easily occur.