I have read on several suppliers websites that their Acoustic Mineral Wool product is twice as effective as ordinary loft insulation because it is denser, but given that a lot of DIY stores offer good discounts (eg buy 1 get 2 free) then what is to stop me putting in a double layer of loft insulation (depth of joists permitting)?
First of all be sure that the noise is coming through the ceiling.
Identify the source of the noise.
If it is traffic or some other ground level source it is unlikely that the noise will be going up and then coming down again through the ceiling.
Probably a brick or block wall to shield the property may bounce the noise away.
If it is the people next door, it will almost certainly be coming through the wall.
Heavy traffic or trains – the noise probably coming up through the foundations.
The next thing is decide what frequency is the most irritating.
If the noise is coming through the ceiling then a pile of insulation in the loft will help.
Consider it may be coming through the windows or walls = aircraft noise.
You may have a hole somewhere?
In this instance the noise is definitely coming from the room below – from a radio turned up high to make a point. The guy who owns the apartment downstairs experienced noise problems from some previous tenants and so whenever prospective purchasers looked round this middle floor apartment (including us) he turned the stereo up high (and put a notice on the door warning there were issues with soundproofing). I’m wondering whether just putting a layer of soundproof matting under the carpet will be enough without having to take up floorboards?
As it is airborne noise then a typical floor insulation will help.
But note: Most of these types are designed for the benefit of the people downstairs, helping to reduce the noises associated with footfall and the movement of furniture.
May I suggest that a word with your local Council would not go amiss. Noise pollution is not tolerated these days. There is absolutely no reason why he should be allowed to make a noise when there are so many types of wireless headphones he can use to get perfect reception and make himself go deaf – it that's what he wants.
In other words you just have an anti-social git downstairs who is taking revenge on you for some alleged slight by your predecessor. He is creating a nuisance. I don't see whay you should have to incur expense to cater for him.
Have you tried discussing it with him? If you are reasonable with him he might just see he is being unreasonable with you by his actions. You could also complain to the managing agent as well.
You could try following the guidance given here Google 'homeoffice.gov.uk/anti-social-behaviour/types-of-asb/nuisance-neighbours/" if all else fails.
Anyway back to your question its difficult to see how you can adequately mitigate this noise problem by mechanical means. I guess you have to experiment. The obvious would be to try some sort of underlayment under the carpet first to see if that improves matters. If that doesn't work then go under the boards.