I'm sorry, but your conception of consumer law is about 200 years out of date.
In a nutshell:
1) Certainly if you are a home user,forget about your warranty. Your printer must last as long as a "reasonable person" would reasonably think it should, considering all factors including the price. This is the main, the most important part of your contract, and overrides the warranty and any unfair exclusion clauses it contains.
2) therefore, nobody can tell you not to use third-party ink. That counts as an unfair exclusion clause because it excludes those reasonable obligations to you implied by the sale of goods act and protected by the unfair terms in consumer contracts regulations.
3) I HAVE HEARDa business can be a consumer, and enjoy similar protections, both under the aboveconsumer law and the unfair contract terms act, which I gather basically says the same thing as the former.
I'm pretty sure this exact case relating to the ink has been written up in case law! Please a lawyer confirm this for me.
The warranty, such as is offered, is a "gratuitous promise" on the part of the retailer (because it's them with whom you have a contract, not the manufacturer) over and above their frankly quite enormous obligations to you under the sale of goods act. The sale of goods act 1893. Yes, that's when it was first written.
The unfair terms in consumer contracts regulations (1985?) essentially states that clauses in form contracts which unfairly deprive the purchaser of utility paid for, can be struck out.