Arthur...the best way IMO is to try and work out the most fair solution possible. Now, fair may not be exactly 50/50. You have to decide what your bottom line is stick with that bottom line. If the adultery means nothing in the UK and is not grounds then you may not have much of an angle to work. I do not know what the law is there but can tell you that in times past the law has been skewed towards mothers/women in the US. That is changing now and in some parts of the US 50/50 is condsidered the norm..
hopefully she will become somewhat reasonable over the next few weeks..your actions and interactions with her may have some impact on that..