Obviously, we can't know exactly why the AI decided to help, but it's not hard to come up with good reasoning.
Central America/Guatemala has been on very friendly terms with GB for the whole game and they are trading partners. GB is (assuming no major political changes) actively anti-slavery and has backed CA's plays against slave nations in the past. CA annexing Cuba would remove a large slave nation from a region of interest.
Another point for GB to get interested especially with France in the picture is that GB and France are really the only big players in the Caribbean. With Central America getting involved and already on good terms with GB, France's interests are threatened by a strong local force allied to GB that could completely kick out France in the future. GB maintains strong control by having CA reliant on their assistance and so would remain as an ally and local force to keep GB's interest safe in the Caribbean.
I have two things to say about this.
First is that if we accept that this is a reasonable explanation (And I believe it is) then we are in agreement that France abandoning its Caribbean allies at the slightest inconvenience is bad, and they should at least receive a war goal to restore the pre-war Cuba (though of course, they could just not go through with it at the final peace negotiations, lots of cases like this).
The second thing I want to talk about however is once again the notion of nations having "friends" and why it is such a flimsy idea. When dealing with politically divided regions empires have two options. The first is to conquer, but if this is unfeasible (as it is in the case of the Caribbean, through some combination of the Monroe Doctrine, the unwillingness of the Metropole population to support such a war, or better targets in China and Africa) they move to the second option, which is to keep the region
divided. Why divided? Why not just pick a friendly government and support them, as Britain does with Central America? It's because it puts you on incredibly shaky ground. All it really is a single cabinet shuffle taking out the pro-British ministers from the Central American government, or people just changing their minds or interests, and your cultivated ally could suddenly become a competitor or even ally of the French! If this happens under normal circumstances, and this sort of thing happens all the time. You can just back Cuba, or Panama, or Costa Rica instead, which is why you kept them mostly divided. But you can't do that when you help your "ally" conquer everything with no assurances. Even actual puppet governments are not safe from this sort of internal change (This is one of my long-term pet peeves with Paradox games though, puppet governments are way too loyal).
Though all of this is quite academic and more of an issue I have with the way people often view history and diplomacy (Ah, yes, Central America and Britain are friends, so of course, Britain won't have a problem with Central American conquests...) and I don't expect any of this to be represented in-game properly.
Lastly, I want to mention that realistically speaking, Britain probably isn't having a consistent foreign policy regarding Central America and the Caribbean. Even if we discount changes in the British government as the result of elections. Most of it would probably be vague, contradictory, "don't screw anything up" sort of idea. And in practice, it would depend heavily on the personal disposition of whichever British diplomat serves as the ambassador in the given country.