It does appear to be one of the bamboos, not sure which- its looking a bit tatty so hard to say which one it might be. The stems on it just look straw coloured at the moment, but if it is a bamboo, those stems should be pretty rigid and hard to break, even if they're dead. As it grows, it might be possible to decide what it is, whether that's a true grass or a bamboo - hopefully, it's one of the Fargesias if its bamboo because they don't run.
Check the area around it to a distance of six feet to start with - you're looking for shoots that might be bamboo, because it might have invaded already. If you can't see any, I would attempt to dig around it, just to see whether it's put out running rhizomes to a good distance under the soil - if it has, then you can assume its one that runs, and if you can remove it, do so. No reason why you can't replant it, but you'd need to insert a rhizome root barrier all around the area you want it to grow, to stop it spreading into areas where you don't want it to.
UPDATE: You've said you're in the UK, in which case its definitely not one of the prairie grasses, and much more likely to be one of the bamboos than any other grass like plant. The strawlike colour of the stems is still odd for a bamboo though, and it looks fairly short, though hard to be sure, but if the stems are rigid that's what it is - it resembles a rather poorly Sasa hyatae, or maybe Pseudosasa japonica otherwise, assuming it isn't very tall.