Bath abandonment

Ughghg. Just filled the bath, got in, decided it needed more hot water, took out the plug to make room for more water, waited a few minutes, water not draining, poked things into the plug hole, nothing blocking it, abandoned bath in favour of shower, tried to get in shower, couldn't get in shower cause my mam put lino down a few weeks ago and its in the way of the shower door which opens outwards. Had to climb over the enclosure. Did lots of angry shouting and banging.

So tonights bath was a complete disaster. I don't know what the hell happened, my first inclination is to think the pipes have frozen, but I don't know if that's a bit too dramatic? I know its baltic out, and its another very icy and snowy winter. But nothing like this has happened before. If anyone can offer any explination please do.
Anyway, we now have a bath full of water that wont drain. I hope it gets sorted soon, I hate showering in winter, especially when I can't get in the goddamn thing.