We have just encountered exactly the same problem with a Samsung washing machine purchased in 2015, the only difference being is that we bought the machine directly from Currys with the so-called 5 year parts and labour warranty. Following many phone calls to Samsung agents reading from the same script we were fobbed off with "Do you have proof of the registration of the warranty" despite giving them the reference number and emailing them all the sale documents including receipt. We then went to the Currys store in Belmont Durham that we bought the machine from and waited in a long line of customers complaining about their warranties not being honoured. We gave all the documents to the staff person dealing with complaints and he said they would be in touch within 72 hours. On the final day we received a letter claiming that our machine was out of warranty but Currys were offering a £144.99 voucher to spend on a new washing machine in full and final settlement as it was uneconomical to repair. When we rang the number to speak to the senders of the letter it was explained that the only route they could offer was the "Out of warranty route" which was a voucher towards the purchase a new one. When I stated that we bought a 5 year parts and labour warranty and wanted it repaired they explained that Currys only cover the first 2 years then the next 3 are supposed to be covered by Samsung. This is a blatant case of mis-selling as none of this was explained at the point of sale and we only bought it because we thought we had 5 years cover. When we explained that the voucher was no good as we would never buy another thing from Currys they offered a direct payment by BACS into our account within a further 72 hours if we accepted it as full and final settlement. So to summarise there are 2 lessons learned here - 1. Currys mis-sell their products with impunity and are not to be trusted so don't buy anything from them and 2. Samsung provide products which do not last as long as advertised and do not honour any "warranties" that they allegedly provide and furthermore have pre-prepared scripts for agents to fend off long and many calls from people who have bought these warranties in good faith so don't buy Samsung products period.
We have learned a costly lesson but like the person above hopefully our bad experience will help other consumers to make the right choice when shopping both in terms of who to buy from and which brands not to touch with a barge pole.