The RAF fighters firing on the ship over London were flying far too slow, and they wouldn't have flown at night. Night time air defence was provided by anti-aircraft guns until radar-equipped night fighters became available - none of which were Spitfires or Hurricanes.
The goof item below may give away important plot points.
When Peter is thrown off the ship by Blackbeard and discovers he can fly, his pendant is nowhere to be seen. Not mid-air, nor while he is floating. He was wearing the pendant when he stood on the plank and also immediately after, when he comes to.