One in seven men in the UK ____ alone.
It seems to me that the predicate 'lives' relates to the subject 'one'. Here 'one' is the third person singular, so we have to add ending '-s' to the stem of the 'live'.
The one man in the subject of the sentence so the third person must be used.
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1/7 men in U.K.hm,a lot of people.
One out of seven. Just one person. He or she, third singular person