During the 60's Britain still had a full brigade of infantry, plus artillery and a Squadron of tanks on Hong Kong. Usually an aircraft carrier was in the far east as well. The defenders would lose (they would have resisted) but it would be a diplomatic "own goal" for China. The "New territories" were leased from China but Hong Kong Island itself was British Sovereign territory and an attack on it would be an act of war.
China would have found itself out in the cold, it's loss of international prestige and trade and the inevitable diplomatic isolation would not have been worth it.
It would have been a short conflict, I doubt very much that it would have escalated any further, certainly no nuclear option would have been considered and no military action to recover the colony possible. Britain would have had immense diplomatic support but no one, not even Britain would have considered a military response other than the resistence of the Hong Kong garrison.
In 1997 Britain handed Hong Kong Island back to the chinese along with the leased territory because they realised it would have been foolish to try to hold on to it, but legally, they had the right to hold on to it.