The Canary Islands are within the EU. (They have separate tax status when it comes to what you can bring back from there without getting clobbered for customs duty but that's not relevant here).
EU law requires all member countries to give free passage to all EU citizens without restrictions. As long as you can prove that you're an EU citizen (by showing your British passport) you MUST be admitted to any EU territory.
While (obviously) you need to have a passport that will be valid on your return date to avoid any problems getting back home, the Spanish authorities couldn't refuse to admit you even if you arrived with just one minute of validity on your passport. That's because, as an EU citizen, you're not obliged to leave the Canary Islands at all. You could live and work there if you chose to do so.
As you've mentioned in your post, a few countries do impose a '6 month passport validity' rule upon visitors but they're very much in a minority. (Even the USA, which has very tight rules about entry and has a '6 month rule' for visitors from most countries, makes an exception for British passport holders). EU member states CAN'T make any such rules in respect of EU citizens (because, as I've stated above, EU citizens are entitled to stay there for ever if they so choose).
The misunderstanding about '6 month rules' comes about because High Street travel agencies couldn't be bothered to train their staff properly and told all their customers that the rule applied to all countries. There are now far fewer High Street travel agencies but, unfortunately, the MYTHS still exist!
YOUR PASSPORT IS VALID FOR ENTRY TO THE CANARY ISLANDS!!!