My $0.02 because my experiences are in Australia and in Taiwan more recently but might help to paint a bigger picture?
I was an authorized Samsung service centre in Australia. We were contracted directly to Samsung Australia, a fully owned branch of Samsung Korea.
This issue would have been rectified even if the TV was one or two years OUT OF warranty, regardless of any third party insurance. I would simply call my contact at Samsung, explain the issue and within minutes they would email an authorisation number to do "whatever I felt needed to be done to keep the customer happy" including replacement of the set if that's what we determined.
In Taiwan, I have purchased many Samsung products because, I foolishly believed they backed their product the same way they did in Australia - not so!!!
One item I bought in Taiwan was a new 80cm curved screen monitor for about US$350. It was great for about a month until I came in one morning to see a 1" wide black stripe down the middle (I never turn my PC off - it screen saves but runs
24/7).
To me, it 'looked like' something had perhaps hit the screen on the edge as it was clear to me the screen was knackered. My office is only accessable by me and I was the last to leave the day before and the first in that morning.
Without the boring in between details about my discussion with the local Samsung agents such as being told "you broke it" etc etc etc I was determined to have it repaired or replaced.
I took The local branch of Samsung to the 'Retail Trade Affairs Office' in Taiwan. Samsung sent a representative from Taipei (a US$120 return trip on the high speed train) not to mention the days wages for her to attend the 'mediation'.
When asked for my input I whipped out the three Samsung issued "Authorised Training Certificates" in my name issued by Samsung Australia directly. This was much to the astonishment of the Samsung representative especially when I said "I bet that I know MORE technical details about this product than the Samsung representative sitting there". She nodded in agreement hahaha
Anyway - they reluctantly agreed to fix it and did - after about six months!
The experience has changed my view of the support they offer for their products in different countries. Since the monitor debacle I have purchased NEW, a 32" TV for a relative, two new phones for myself and my wife, 2 x new refrigerators, a freezer and a washing machine.
I made a point of making sure that NOT ONE of these products was a Samsung MAINLY because I wanted to contact Samsung Korea to tell my WHOLE story and there is NO CONTACT information for them anywhere!! No fax, email, phone NOTHING!!! So I bought other brands.
My advice, not having a clue about consumer laws in the UK, is to scream long and loud - to the point of paying a small consultation fee to a solicitor - get them to send a letter demanding a resolution to your satisfaction. If the local Govt consumer dept didn't take up my case, my next step here was a solicitors letter and, by this time, I was furious and was not going to let them get away with NOT honoring their warranty.
Best of luck with it and be sure to tell friends and family of your warranty experience, it matters that people know far and wide.