That must be horrible to live with.
Just a thought, but did you buy this as a new house directly from the developer ?
If so then you have powerful rights under the Sale of Goods and Services 1982 - this amends the earlier 1979 act, and is itself amended by The Sale and Supply of Goods to Consumers Regulations 2002
http://www.which.co.uk/consumer-rig...complain-to-companies/consumer-law-a-summary/
One option is to go to Trading Standards, though these days you have to go through a call centre where I consider them to be handing out completely useless advice - you aren't allowed to contact your local office directly it seems. At least that was the case last time I tried.
Alternatively ...
Now, whether the rest of this post is helpful does rather depend on your appetite for "having a go" ...
The key terms are that goods must be fit for the purpose they were sold, and must be reasonably durable. Unless the seller can show that you have done something to cause the problem (for example letting excessive amounts of water be spilled on the floor, which I assume you haven't) then it would be very hard to claim that the floor in your pictures is either fit for purpose or has been reasonably durable.
The question to consider is "how much will it cost to put right ?" I say this because the builder has already been given the opportunity to put it right but has refused - that rather suggests that it may have to "get legal" before he will (or for you to get cash from him to pay for it to be done properly). If the claim doesn't exceed £5,000 then it can go through the "small claims court" (I think it's correct name is the "small claims track of the county court") which is designed to be easy and simple for people to use. Even if the cost would be over £5k, it may be worth only asking for £5k as the procedure (and potential costs) change considerably above that.
The key thing would be that you'd need some evidence that there was a fault and that it wasn't your fault. Normally I'd say that your photos would be enough, but you'd need to counter the opinion of the NHBC report which says it's OK.
It may be worth sending your photos to Sid Bourne (never heard of him myself (not surprising as I work in IT, not building), but the others seem to rate him) and see if you can get an opinion from him. He may be prepared to offer a preliminary opinion based on the photos for a modest fee, as well as giving you a cost to come and visit the house to see for himself. If it goes to court, then he would almost certainly need to do so before giving evidence.
Armed with that, I'd be tempted to download the court forms, fill them in, but don't send them in yet. Send copies of them, and the opinion from Sid Bourne, and a covering letter stating that :
a) You consider the floor to be unfit for purpose and not reasonably durable, as required by the Supply of Goods and Services Act 1982.
b) You have an opinion from an expert supporting this view.
c) You expect him to put the floor right at his own expense, or pay for someone else to do so. Set a reasonable timescale - give him 14 days to reply, and 28 days to complete the work.
d) If he fails to do so, you will instigate proceedings in the County Court.
e) In court, you will ask the judge to compel the builder to disclose the manufacturer of the flooring so that you can contact them.
f) You will also be calling the expert witness and will expect his costs to be met by the builder.
Send the letter recorded delivery so he cannot claim not to have received it - though by law, if you post a letter by Royal Mail, then it is deemed to have been delivered next day if first class, and after 3 days if second class (proof of posting is proof of delivery by law !)
My guess is that the builder will instantly change his tune, or will as soon as he's served court papers. Unless he's a complete idiot he'll realise that unless the manufacturer says the installation method is acceptable then he'll have no defence whatsoever and he will lose the case. He cannot refuse to provide the manufacturer's name if the judge asks for it - otherwise he is in contempt of court and the judge can lock him up ! The fact that he's refused to name the supplier does suggest that he knows the floor wasn't installed according to the instructions and doesn't want you to find this out by getting the installation instructions or an opinion from the manufacturer.
I would suggest that unless you are of a particularly strong constitution then you might want to find someone to help you with all this.
The actual legislation can be found at these links - if you enjoy a dry read !
Sale of Goods Act 1979
Supply of Goods and Services Act 1982
The Sale and Supply of Goods to Consumers Regulations 2002