I have met the same problem, and a solution was to add

BEGIN {
$ENV{PERL_LWP_USE_HTTP_10} = 1;
}
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or examining LWP/UserAgent.pm

if ($ENV{PERL_LWP_USE_HTTP_10}) {
    require LWP::Protocol::http10;
    LWP::Protocol::implementor('http', 'LWP::Protocol::http10');
    eval {
        require LWP::Protocol::https10;
        LWP::Protocol::implementor('https', 'LWP::Protocol::https10');
    };
}
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to add the lines enclosed in the if statement directly. Cheers.