I'm in a similar position - although my H hasn't been unfaithful, we've come to the end of our 17 year marriage - decision made this weekend. We own our home, but he has agreed to move out and i'll stay there with our 2 DC - he's now looking for somewhere to rent.
I earn £20K and he's on approx. £14K so I'll be entitled to extra Tax credits. I've contacted the Tax Credit office today and they said that it can take up to 3 weeks to process a change in circumstances. I asked if I could start the process before he actually moves out, but they were very vague and I didn't get a proper answer to be honest.
You do need to show that the separation is 'likely to be permanent' - however they wouldn't give any examples of how you can show this (useful!!) You can inform them of a change of circumstances online now - you just need to register for a .gov.uk username
My (our) plan is to sever ALL financial ties as soon as possible - I've made a 'to do' list - which includes H opening a new current account, changing where his salary is paid into - removing him from Credit Card Account, changing home insurance, change his address at Dr's, etc etc, and hopefully this will all be enough to show that we are separated.
the only thing we plan on leaving joint for the moment is the mortgage as we'll need time to work out what to do about that, but I'm hoping that that won't affect the Tax Credit change, as I'll need the extra money from that to be able to pay the mortgage.
I'm trying to be as calm as possible and think about things rationally and practically, and the to do list is helping with that. I've also got lots of information from www.sortingoutseparation.org.uk - which is really useful.
Best of luck - hope you manage to sort everything out