Yes, I know Interpol can't be called by the public. If they thought there were links with organised crime routes (U.K./ Spain/ beyond), though, they would indeed communicate with Interpol, certainly when something has become high profile enough to interfere with business, which this definitely has.
Culturally it is quite different from here to Southern Spain and the Canary Islands. Can you give me an example of a high-profile case where a Spanish national has been lost or killed or wanted for a crime here, and the U.K. police have not managed to sort things out? I can't think of one off the top of my head but that may have more to do with how business and the movement of people happen differently in different parts of Europe than with our forces being especially competent. If you can think of a few cases like that, or even one case, we could have a look and see if we can answer your question. I bet they do exist!
I can only think of cases that were solved pretty promptly. We had two murders here committed by non-U.K. E.U. nationals within 24 hours of each other, Eleni Pachou and Moira Jones. One of the murderers was from Canarias, and Eleni was Greek. Moira's killer was Slovakian and they had to go and get him under a European arrest warrant. There was also the case of Karen Buckley a few years ago. Of course, the U.K. was still in the E.U. during these cases, which might have implications for communication.