There was nothing for it but to wait until the next morning.
Literal
Next-morning until wait [no-choice-but-しかなかった].
~しかない ('have no choice but to / the only option is') is a fixed pattern using しか ('only,' which requires a negative) + ない. Attached to a verb, it conveys 'the only thing to do is X.' In past form ~しかなかった = 'had no choice but to.'