The videos comes on with the play symbol, but the timeline has stopped appearing, so when I press play, it just buffers. This problem has only just happened.
I'd check whether or not you have iCloud Photo Library space saving feature turned on.
If so, it may be uploading your videos to the cloud and then streaming them to save space on device.
I'd assume you have mobile data turned off or have a weak signal which is causing the videos to buffer and not play.