You're not a failure as a mum. It won't help for this year but after Christmas look out for people selling decorations or plastic fake trees on FB so you'll have something for next year.
For this year make paper chains or make snowflakes by folding paper in half and cutting bits out of it. That's a bad explanation but there's probably a YouTube video somewhere.
Go food shopping Christmas Eve for discounted treat food.
Go to a charity shop for some DVDs of Christmas films or perhaps there will be some on TV anyway?
Go for a walk to your local park on Christmas Day, half the population of the UK will be doing this so you'll be no different to anyone else.
Go to midnight mass on Christmas Eve or another church service locally.
Put the radio on, some channel will be playing Christmas tunes.
You're feeling it worse at the moment because you've just had a breakup. You can still have a Christmas of some sort though. If you want company, think of who else you know without family around and invite them over. Not for dinner if you can't afford to feed them but just to watch a film or something or to join you on the walk.