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This figure was the most striking from its findings, the adviser directory business suggested, as this age group were most likely to have dependants and other major financial commitments, such as mortgages.
More than a third (37%) of those aged 55 and over did not have a will either, the research found, while more than four-fifths (84%) of those aged 18 to 34 were in the same boat.
This number surpassed the previous peak in 2011, when similar research by Unbiased indicated more than 29.5 million UK adults did not have a will. This time round, through Opinium Research, Unbiased surveyed some 2,000 UK adults in September 2017.
Procrastination was found to be the principal reason why people had not made a will, with more than a quarter (26%) of respondents saying they planned to make a will later in life.
More than a fifth believed they did not have enough assets to make a will worthwhile, while one in 10 (11%) said they were put off by the cost of writing a will.
Unbiased found adults in Liverpool were the most likely to have no arrangements, with nearly three-quarters (73%) saying they did not have a will. Not far behind were Nottingham (69%) and Glasgow (68%).
Of those who had made a will, individuals expected to leave an average of £227,000 in property and £74,000 in monetary savings to loved ones when they died. Unbiased found property assets had steadily risen since 2015 - up by £5,000, from £222,000.
It also found average savings to be passed on via will assets had dropped £2,000, from £76,000 in 2016 to £74,000 in 2017.
Unbiased chief executive Karen Barrett (pictured) said: "The huge benefits of having a will, and the even bigger risks of not having one, should be far more widely known and talked about. People think a will is just for the end of their life, and it is - but who knows when that will be?"
She added: "It is clear many people think they're just not ‘rich enough' to need a will. This ignores the fact a will makes inheritance a far quicker process - do they really want to keep their loved ones waiting longer, when that money might be badly needed?
"It also doesn't take into account the complexity of modern families, which intestacy law simply doesn't address. Children from previous marriages could end up receiving nothing at all."