Well, I hate to say it, but he's right, and if there is any justice in the UK, then he is going to win. All references about "The Land Of Lawsuits" aside, this isn't simply because I'm sue crazy as an American, but because this is a legitimate issue (unlike many cases in the US where there isn't one, at least to an outside observer).
At the end of the day the bottom line is that his father was awarded "rights" which eventually transferred to him. This means he has some documentation as to the claim, and these rights have been officially tracked through their transfer. This means an actual, acknowledged IP exists here, and has been transferred.
Now, whether the rights holder chose to be assertive before now is more or less irrelevant, especially if some kind of gentleman's agreement was apparently in play with the previous generation of the family. Legally speaking, the TARDIS belongs to this guy now, and he's a part owner of the "Doctor Who" IP as a result. Indeed it could be argued that the Doctor Who rights holders might be guilty of fraud if they filed a copyright knowing that someone else had documented rights to this particular aspect of the mythology.
To put things into perspective, it's sort of like a case in comics where a specific creator owns a character even if he doesn't own the rest of a publisher's continuity. If he leaves, he can take his work with him. Nowadays you see this happening less often due to the legal battles that have taken place in the past, publishers watch their back more, but if you listen to some of the stuff in Moviebob's "Comics Are Weird" segements of "The Big Picture" which have involved the storied past of characters like "Marvelman" (or Miracleman if you prefer), and explained the whole mess of issues that came up when a creator wanted to use his "Angela" character in Marvel, and what that meant behind the scenes... you can sort of see where this is going.
Right now since these rights apparently transferred legally after the 1980 copyright, they still existed, and were acknowledged as being valid.
This case is pretty much the rights holder of a character (in this case a ship) demanding the publisher pay royalties on continued use of that character. The case for retroactive payment also kind of stands up, as it wouldn't be the first time someone realized that they had rights to something from an estate that someone else was using without realizing they did not have the rights to do so. Albiet in this case it's intentional and premeditated, as opposed to something someone discovered after the fact.
Honestly I expect this will probably be resolved quietly, whomever holds Doctor Who's primary copyright will probably realized they "oopsed" and hand the guy a few million pounds to buy the rights outright so they can own them free and clear. Largely because even if they go to court and win, it will put a shadow over the entire thing, legally, if not in the minds of the fans. Later on if another rights question come up, even a victory here can be used to paint them as rather shady.
That said, at least it's not as bad as some IPs which will likely never return because it's nearly impossible after the fact to determine who exactly owns what. In apparently the entire run of Doctor Who, it's actually pretty good that this is the only suit of it's kind (or at least I think it is) given the sheer number of writers, actors, directors, and producers over the many, many years of it's run.
