I've got an offer to do a PhD at a great uni in the UK, in a scientific topic I find really interesting because of some courses I've taken at Master's level.
My dissertation advisor seems to think that being interested in a topic isn't strong enough as a motivation, and that I should be passionate about the topic and have a clear idea of why I want to study it and what it will lead me into.
I wouldn't say I'm passionate about this topic, but I wouldn't say I've studied anything in enough detail to be passionate about anything in particular yet. All I know is that I found this topic interesting and stimulating. People usually get passionate about things when they start doing them at a really high level, which I haven't had a chance to do yet.
Regarding what it would lead me into - I don't know exactly what I want to do in life yet, but research really appeals to me, and so does academia.
Is this reason enough to accept the offer, or should I reject it and wait until I become passionate about a particular area and know exactly what I want to do in life?
To be a bit snarky towards your professor, I don't think that we can truly answer this question until we have some sort of passion-ometer that can distinguish degrees of caring. How much interest is "enough" is just not quantifiable.
That said, there really does seem to be a qualitative difference in how people do in a Ph.D. based on their degree of motivation to be in the program. There are lots of good things to do with one's life that are much more short-term rewarding than doing a Ph.D. Thus, people who enter a Ph.D. program just because it seems like a reasonable next thing to do with their lives are likely to run into difficulty and end up exiting to one of those other nice alternatives. People who are having trouble but do not have alternatives and feel trapped in their program (e.g., due to visa issues) are at a strong risk for harm to themselves or others, up to and including suicide or violence.
But passion for a particular topic isn't a make or break. I think the key is whether a person finds the ongoing struggle of research rewarding. If you find that you have a taste for that, a Ph.D. is a good idea; if you don't, it's probably a bad idea.
And it's difficult to really know until you've really engaged with some big research or engineering projects. If you have, you probably know if you've enjoyed them enough to make a life out of it, whether you stick with a particular topic or end up shifting over time (as most active researchers do eventually, as their original topics either succeed or hit dead ends). If you haven't ever really engaged with research before, I would recommend getting involved in some research first before making the longer commitment to a Ph.D.---although a 3-year UK Ph.D. is short and focused enough that such a preface might not be necessary.