Europe does not have as stringent consumer laws as the UK. Sale of Goods Act doesn't apply for products bought outside of the UK. Warranty claims may have to be dealt with in country of purchase etc.
You pay the money, you take the chance.
The Sale of Goods Act is a UK law but the same/similar concept exist which says that the retailer has to replace or repair the faulty goods. I found a good summary and relevant links
HERE.
If you bought your item online
Online sellers from other EU countries may target their products or services to the UK market. For example, by offering prices in Sterling and delivery options to the UK. If you buy from such a seller online and something goes wrong, you can argue that your UK statutory rights apply to the contract despite it being subject to the laws of another country.
So, if you purchased your item online from a trader from another EU country, then you should be protected by the Consumer Contracts Regulations, which is the UK law that implements the EU Directive entitled the Consumer Rights Directive.
In essence, to a certain extent the buyer's country's specific laws are recognised in favour of the consumer.
Also remember the manufacturers warranties only cover repair. Any replacement doesn't have to be new so could well be a refurb.
Looking at the relevant laws, it looks like the Consumer Contract Regulations that came into effect on 13 Jun 2014 gives you the same rights as you would purchase products in the UK under the Sale of Goods Act. Quote from
HERE:
Returning faulty goods
If you receive faulty goods and wish to return them, The Consumer Contracts Regulations are in addition to your other legal rights. So, if your goods are faulty and don’t do what they're supposed to, or don’t match the description given, you have the same consumer rights under the Sale of Goods Act as you have when buying in store. Any terms and conditions that say you must cover the cost of returning an item wouldn’t apply where the goods being returned are faulty
When it comes to warranties, those are separate contracts! The warranty may have nothing to do with the seller. For example, a friend of mine had a Lenovo laptop that developed a fault and was replaced in Europe although the product was purchased in the US. Basically, there are two sets of protections 1) with the retailer and 2) manufacturer if there is specific warranty.
What I am not sure whether let's say a Samsung monitor purchased in Germany will be repaired and if needed replaced in the UK (or the other way around) under the manufacturer warranty if a problem develops.
Here is a quote from the Samsung Warranty related to Monitors (24 months):
Samsung Electronics (UK) Ltd support a product purchased in Europe if it has an EU Bloc Warranty. This warranty is present where the top of the product warranty card clearly states 'European Bloc'. If the product is purchased in another part of the globe then Samsung may attempt a repair. Samsung Electronics (UK) Ltd cannot guarantee the outcome.*
*Note that Samsung even attempts to repair products under warranty purchased outside of the EU.