With the British weather you never really know what you are going to get! IF on the day we book the weather is awful I will always rearrange. There is no point trying to force a session in poor weather as you will not get the best result.
I generally avoid doing outdoor family sessions between November and February as the weather is generally cold, miserable and the landscape is dull. As a result, I am usually super busy from April through to October running around outside with families capturing family life.
With regard to times, I typically do early morning to take advantage of the soft natural light (9 - 9.30am start) but if you've got little ones who still nap I can tailor it around their "normal" nap times (I say that tentatively!) to get the best out of them.
In the height of summer, I also do evening sessions as the sun casts a beautiful warm soft glow. Evening sessions are ideal if you have slightly older children or little ones who enjoy being up past their bedtime!