Hi, OK, so here it is.
I'm a final year biological sciences student and I want to do a PhD when I graduate. I've been speaking to one of my lecturers and he thinks he might have one, and it's in my general area of interest which is good. However, he's never very forthcoming with specific details like the exact topic or if he'll be able to get funding.
I also did a placement and my undergrad project at a local research lab, and they also have PhDs available. Two of them are on the same topic and with the same supervisor as my undergrad project (with funding) and I really want to apply for them, but my dilemma is this: both institutions and lecturers communicate a lot, and so do you think they will be annoyed, or even less likely to take me on, if either find out I've applied at the other place?
Any advice would be great! Thanks.

they will hopefully understand that you need to keep your options open.

also, it may encourage the university to get a move on with the funding etc, to prevent them from losing a potentially good student to the other project.

I think you should apply to the local labs, as the PhDs there are likely to be quickly filled, but also the projects will be well defined and you will be in a good position to stay on with a job afterwards.

Why not talk to your other lecturer and see what he thinks about recommending you for the place. In which case you might be able to set up a collaborative project with him as your 2nd supervisor?