What would be considered a "best way" to approach this would have to depend on what your wife's expectations are. She had asked for no contact and you had respected that but there has to be a time frame and she can not hold you in limbo indefinitely. You and her would have to set up some goals that each one can work on individually during your no contact period. You can own the issues you were responsible for that led to the separation while she does the same on her end. The two of you would have to come up with short term goals- what do you want to get out of this period, how you and she can work on improving those factors within yourself that led to the discord in the first place, engage in self introspection and consider seeking individual counseling to get some objective feedback, etc.
After the no contact period is over and the two of you start talking again, you would want to set up goals for the relationship (if you and she had decided to give it another try) There is always the possibility that she decides not to reunite with you but you have to cross that bridge when you get there. For the time being, both have to remain focused on the present moment and what can be achieved at this time. Should she decide to give the relationship another chance, both of you would decide on how to start working on the reunification together ex: working with a family counselor/coach, going to a marriage camp, etc. The two of you have to be active in working on a resolution. Simply not keeping in touch is counter productive unless you and she is using this time for self improvement/making the needed changes. Both have to know what each one expects of the other and of the relationship as a whole. The issues that led to the separation/friction have to be dealt with. They are in the past but if not addressed, they can resurface again.
As far as the literature out there, you can use it as you see fit. There is no one book that would offer an instant fix but some of the books give you an idea of what you can do to change within yourself that may be something she wants. The books would rarely offer you the secret of how to make her feel anything she's not already willing to feel. Actions always speak louder than words. She would want to see some different response from you than what you've done in the past to cause her to want to split. You can always ask her about that when the two of you start communicating.
I've opted out. From the question, it was not clear that the location of the expert was an issue. It appeared you were seeking objective feedback versus resources in UK. or UK experts.