The Entente Cordiale was a very recent and in some ways quixotically signed alliance, along with the treaty with Russia; while Britain had previously aligned with France in the Crimean War, the latter part was as unexpected as the modern US allying with Iran against Pakistan, for example - Russia had been Enemy No. 1 for much of the 19th century. So whereas the Entente was very much an alliance of convenience, aimed at British (and particularly Edward VII's) analysis of who was the most dangerous threat in Europe right now at this moment, i.e., Germany, the Anglo-Japanese alliance was on another level. Inaccurately in retrospect, Britain more or less believed the Japanese to be the safe little yellow cousins we could trust not to switch sides. So an Anglo-Japanese effort is certainly more likely than an Entente one to my mind, but I have a feeling that space efforts would really be one per country, with only token cooperation across alliance lines. After all, it isn't as though there was a NATO and a Warsaw Pact space programme in OTL.
One interesting aspect is that a British space programme, rather than being based out of Woomera, Australia, as in OTL, will probably be based in equatorial India...