Hi ya . I'm not certain there's much experience of MG3 on this forum but I could be wrong . Don't all MG's come with 7 Yr warranties these days ? I could only guess that maybe the diff shims have broken , but that is purely a guess . Hope you get it sorted .
John .
I too have no experience of the MG3 but a starting point might be to check the engine mountings, a failure here might impede the shift mechanism from working properly
"Keep calm, relax, focus on the problem & PULL THE BLOODY TRIGGER"