The Sales of Goods Act should cover this - it would be considered "reasonable" in the legal sense that a £350 BD player should be fit for purpose for far more than a year or two - under the act you can make a claim with the retailer for up to six years after purchase in England and Wales or five in Scotland. Rather ambiguously the act says that goods should last "a reasonable time" - that may only be considered a year for a £7 Tesco's toaster but obviously far more for an expensive piece of electronics like a top of the range BD player like yours - I'd say up to the prescribed full six years in normal circumstances.
Your contract is with the retailer, who ideally should fix it at no cost to you. If they can fix yours with parts from another machine, and it functions perfectly well and as you'd expect, then I'd say that's fine and a good solution all round. You can still make further claims with the retailer if the BD player breaks down again within its "reasonable" lifespan, although obviously the older it gets, the harder this is to pursue (relatively easy at two years old, much harder at six). If the retailer wants to charge you for the fix (or indeed charge anything you're not happy with) or fail to fix the player properly or to your satisfaction, you need to press them further, ultimately with the threat of a Small Claims Court action if need be. However, it does sound like the retailer is playing ball so far so hopefully that won't be necessary - always easiest to sort these sorts of things out amicably.
While the retailer is legally responsible for sorting this out, it's a shame the manufacturer has taken such little interest in helping you - it's potentially very poor publicity for them, both in the quality of the product and their after sales service.