The British initially intervened with the French in Mexico. Once France exhibited its intention to stay, the British protested and stepped back from their, at this time, ally's actions. The French found their scheme untenable in the face of growing British and American protests, the failure to quash the Mexican resistance and the threat posed by the end of the US Civil War.
The Chincha Island and Santo Domingo conflicts were a result of Spain trying to re-emerge onto the world stage. The British protested in both cases. However why interfere with the European power's foolish and likely unsuccessful attempt to bully the fprmer colonies. Santo Domingo was Spain trying to recover a small former colony, which failed without intervention. Again the end of the US Civil War was a factor.
The Chincha Islands was a foolish and counter productive display of power. The nations of Chile, Bolivia, Ecuador and Peru would have welcomed friendly relations with Spain. Spain was unable to project power in the area once Colombia closed its ports. The former colonies were now real nations, with their navies, armies and foreign alliances. The US and British navies protested the Spanish blockade due to its effect on trade.
In both cases, actual physical interference by Britain or the US was unnecessary. I would have liked to see result of an encounter between the Spanish fleet and the Allied fleet once Huascar and Independencia were ready to join the fight. I would expect a costly Pyrrhic victory for the Spanish.