Thanks for the feedback everyone!
TreeofLife - yes, my supervisor did express that having me follow would be desirable, so I have someone vouching.
chickpea - it is a research council studentship, but in collaboration with my uni. That seems to be the sticking point right now! Luckily, the move is within the country (and not very far) so hopefully we can make it work.
Mark_B - Thank you for your insight. Good to know that it is an option. It is still early days in terms of negotiating this, so hopefully it ends well. I would hate to lose this supervisor, but worst case is I move on with someone else.