LONDON, July 12 (Reuters) - Britain must introduce tougher policies to make residential heating more efficient and consumers need to cut energy usage to meet the nation's target of net zero emissions by mid century, the National Grid said in a report released on Monday.

The National Grid Electricity System Operator (ESO), which distributes power around the country, modelled different scenarios in its report, with three showing how Britain could meet its goal in 2050 or sooner and fourth that misses it.

A cross-party group of lawmakers also said last week the government needed do more to engage the public and should publish policy plans on how it aimed to meet its net zero emissions target.

In the National Grid various scenarios, Britain could by 2050 have up to 37.4 million electric vehicles on the road and road transport energy demand could fall by 60%. Britain could also have negative emissions from power generation by 2034, if carbon capture was included.

Green hydrogen -- or gas made by splitting water via electrolysis using wind, solar or another renewable energy source -- could play a role in achieving net zero emissions, according to scenarios in the report.

But the report said society also had to change.

In the most ambitious scenario, households in 2050 would turn down their heating thermostats by an average of 1 degree Celsius and more than 80% would be charging electric vehicles using off-peak power. The scenario also envisaged no natural gas consumption without carbon capture and storage after 2035.

"Consumers will need a greater understanding of how their power use and lifestyle choices impact how sustainable our energy system will be," said Matthew Wright, head of strategy and regulation at National Grid ESO.

"Government policy will be key to driving awareness and change," he added.

(Reporting by Nina Chestney; Editing by Edmund Blair)