Perhaps you are
I'm vibrant life where there is death,
Poppies are brightly coloured living things, even though they (1) are used for remembering people who died in war and (2) this is (I think) because they grew abundantly in some places where there were awful battles in the First World War.
Even though I have no breath,
They're plants :-).
Double elev'ns I'm held to breast,
Particularly used to commemorate the end of the First World War, on the 11th of November (the 11th month).
And then in winter, I have my rest,
Like many plants they grow actively in the warmer parts of the year and only their seeds remain in the winter.
Though I remember heroes,
Commemorating the dead of WW1 and other wars.
It is criminals that remember me,
Not sure what this is about, but see below.
I give solace where there is pain,
I help reach for heaven, but in vain.
Poppies are a source of opiate drugs. Some are very effective painkillers. Some are powerfully euphoric but tend to lead to addiction and messed-up lives. (So perhaps the criminals a few lines above are drug dealers.)