Ultimately, the British Government traded The Belfast for Chen Yu's promise to help them transform the HMS Victory into a ship-girl.
Although it meant losing face, gaining a true demigod not bound by a lifespan was a real bargain for the British Government. After all, lost pride can be forgotten, but tangible benefits signify a profit.
Moreover, even though Hood's appearance caused quite a stir, she was, no matter how you look at it, a British ship. As long as the media didn't spread rumors and the truth was well concealed, the lost pride might even be recoverable.
Chen Yu had no interest in the British plans. After handing over The Belfast to the United Kingdom, he returned to his Necromantic Space with Artoria, Joan of Arc, and the others in tow.