my young daughter will have just 4 months left on her passport when we go from cyprus to uk and then back again will it be ok
I'm not clear on what you say about the timing but if the passport is still valid it's valid. If the passport expires while you're out of the country it depends on how sticky the border guards are and the immigration officials want to be. I didn't realize it once when I was traveling in Europe but my passport expired. The Canadian immigration officer pointed it out to me when I returned home and suggested I get a new passport and that was the only difficulty I had with it. I was pretty lucky.
You need to read this web page from the British Home Office to find the answer to your question. There are several factors that come into play such as the age of your daughter.
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Other people asked questions on various topics, and are still waiting for answer. Would be great if you can take a sec and answer them