Don't.
It's not just about the money - you are enabling her, rescuing her from the consequences of her actions in a way which means that she just won't have to regret any of it at all - she's going to be in an even better position than if she had it on a credit card... no interest, no penalties, not even having to pay it back if she squeezes out a few tears.
So give her two years and you'll be here again. Only difference is that you'll be poorer.
And you'll resent her for it, it will affect your relationship. Even if you can afford it - which it doesn't really sound like you can. What happens if there's an emergency your end? - your DH loses his job, unexpected expenses crop up?
Help her, but not by bailing her out. First step - can you go to Shelter and see if anything can be done about a pay plan for arrears? It will take them a LONG time to evict her if they go down that formal route anyway - get involved, get advice, see if there is any way she can start paying once she starts her job.
Look into the possibility of her earning some cash some other ways.
Make her go to the GP and get on the list for counselling - or, if you want to spend money on this, get her private counselling. This problem will not go away, by payign off her debts you aren't solving the issue. Nobody wothout a serious problem spends their money on crap online when they haven't paid their rent. Sorting this for her only kicks the can down the road.