I've just finished a BSc and got a lower 2 in Biomedicine. Does anyone know of whether it's still possible for me to apply to either a MRes or a PhD? Wanting to go into further studies but need to know what sort of options I've got

Your best chance is with an MSc. MRes usually ask at least a 2i as do PhDs. As it's been said in previous threads, an MSc usually boosts your 2ii to the equivalent of a 2i. You can then go on from there should you wish to.