The fund manager recently instigated a major drive on climate change with its investee companies and increased the number it actively engages ten-fold to 1,000.
L&G said it had specifically targeted 58 companies of which three-quarters had responded and 13 now had a net-zero target in place.
Voting sanctions are imposed for companies that do not meet minimum standards, it said, such as having board members with responsibility for climate issues, comprehensive carbon disclosures and greenhouse gas reduction programme, LGIM said.
Michelle Scrimgeour, chief executive, called on other fund managers to follow its lead.
"Progress cannot be made by acting in isolation and we, as investors, have a real role to play in the responsible allocation of capital and acting as stewards to our investee companies to encourage greater progress to meet our overall sustainability goals."
Investment arm LGIM has also axed four companies from its portfolios because of an insufficient response to climate change issues.
The companies, two of which are US businesses and two Chinese, are insurance giant AIG, utility PPL and Commercial Bank of China and Mengniu Dairy.
All four had breached or not reacted to a red line warning over their involvement in the coal sector, carbon disclosures or links to deforestation, said the statement.
"We've been making consistent requests for a multi-year period ... [the companies are] really not meeting what we consider to be baseline minimum standard expectations in terms of climate change management across their sectors," said Yasmine Svan, senior sustainability analyst at LGIM.
L&G, which is the UK’s largest institutional investor, has already dropped nine other companies, including Exxon, for similar failings.