The level of detail is clear from the format: it's a 15 minute presentation with some time for questions, so I won't have time to talk in much detail, but I might be asked to elaborate on any aspect of it. All in all, I am a fair deal nervous, and I'm not even sure I'm asking the right questions here; any advice from the perspective of applying for a first-time faculty position would be great.
I see from comments that the interview is past, but here's still some thoughts on this that might be useful for someone else.
I would say that your results at a 3-years horizon don't depend that much on funding prospects, mainly because you're not starting with those funds from day 1, and as a new lecturer you're certainly not expected to have an army of postdocs working for you in the first couple of years.
You might spend a few months writing the grant proposal, then the process will take some more months, and then from decision to start date there's more time. so assuming success you might be able to hire someone to start in a year at best, more realistically two. Then would you start immediately with postdocs? Unless you're one of several investigators in a larger project, that doesn't sound realistic. Rather you'll probably be supervising MSc projects, and you might hope for one or two PhD students to start within those three years, and with any luck get their first paper or two. I think what you need to pitch is a set of ideas that could form a grant proposal and some realistic-sounding MSc and PhD topics.
The bottom line is that you're being asked for a 3-year plan to see whether you can actually prepare a plan that involves medium- to long-term goals, rather than just think of the next development of what you're doing at the moment.
answered Nov 7, 2018 at 15:34 user3780968 user3780968 1,430 1 1 gold badge 10 10 silver badges 13 13 bronze badgesMy situation was a bit different as I went directly from my mathematics PhD to a faculty position (in the US). But when I finished the doctorate I had a file drawer full of speculative ideas and ideas left unexplored from the work on the dissertation. If you have such a thing, or could create it, you should 'mine' it for ideas that are yet to be explored. These should be easy for you to discuss since you already touched on them in your past, though if you haven't already recorded them you have some work to do. For such work you can probably speak with confidence.
Fifteen minutes isn't very long, so you don't need a lot of material. But you might think about the fact that since you will also be teaching, research that students could potentially participate in could be especially valued. Also, you have likely gained insight into a wide range of ideas that are at least peripherally related to your current research. That wide range opens doors to a moderately broad "area" of research that increases your likelihood of success in exploring at least some of the ideas. While research is necessarily narrow for a given idea, there are related areas, most likely, that increase your range and hence your desirability as a colleague.
Sorry that I can't speak much about UK funding, but in general, "interesting" ideas are also interesting to funders. Likewise, appearing to a funder as someone with a lot of ideas (and therefore potential) is also an advantage.