The most important philosophers?

Oh yes, I agree with that - it is good evidence confirming what we might anyway have suspected about which philosophers are nowadays taken seriously (at least by a certain kind of philosopher). In a way that is just my point too. I just meant it is pointless qua evidence for which philosophers are genuinely important, at least from a historical point of view.

I do by the way think that if by "important" one means "influential" - so, without understanding a certain figure and his or her impact, you cannot understand what came after, and having a long chronological impact - then it is not just a nebulous matter of opinion how important a given thinker is. Obviously this is not easy to determine, but no one could plausibly argue that Speusippus was more influential than Plato, just to take an extreme example. Or to take another extreme example: if someone denies that Aristotle is the most influential Western philosopher of all time, they are just betraying that they don't know what they are talking about (unless they say it is Plato but then they would have to add that Plato is influential through Aristotle). Of course the chronological duration of impact favors ancient thinkers, and if you discount this then perhaps you could argue that e.g. Avicenna or Kant has had as massive an impact on subsequent developments as Aristotle. But there are still facts of the matter here.

A comparable project was launched a few years back by the BBC, where people were asked (if memory serves) to name their "favorite" philosopher. Marx won (!).

Well, that's a pretty traditional list and I wouldn't say any of them are overrated! But on the other hand one can see from this list the problems of this kind of "great figure" approach to philosophy: these are all European men, and you are sort of assuming in advance what will count as important (basically, systematic metaphysics and epistemology... plus Socrates). Even if we accept those priorities then Ibn Sina (Avicenna) is as influential as anyone on here apart from Aristotle. If we remind ourselves that Europe is not the world we might consider putting, say, Confucius or the Buddha or Nagarjuna on there. If we think that thinking about the situation of women is not philosophically irrelevant, we might put, say, Christine de Pizan on there.

But actually my main advice would be to stop thinking in terms of greatest thinkers. Even the people on this list can only be understood by comparing them with predecessors or contemporaries who are not so famous, e.g. Plotinus' own contemporaries accused him of stealing all his ideas from Numenius (probably an unfair accusation but it still gives one pause). You do need to start somewhere of course but I would encourage you to think more in terms of philosophical problems or traditions, and not individual great men.