The measures are outlined in the Vehicle Technology and Aviation Bill.
Ministers says they want to ensure it is easy for accident victims to claim compensation if a collision occurs when the cars are in automatic mode.
Insurers could still try to recover their costs from the vehicles' makers.
However, the bill - which applies to England, Scotland and Wales but not Northern Ireland - makes two exemptions.
If a vehicle's owner has made unauthorised changes to the car's software or fails to install an update that their policy requires them to, then they become liable.
It is proposed the Department of Transport will determine which cars will be classed as self-driving and become subject to the requirements.
The suggestions have been welcomed by the insurance industry.
"It demonstrates the government's clear commitment to moving forward when it comes to automated vehicles," said Ben Howarth, senior policy adviser at the Association of British Insurers.
"As an industry, we want to keep insurance as straightforward as possible, which is why insurers proposed the simple approach which the government is now taking forward."
Self-driving cars are already being tested on UK roads.
But many car companies predict it will be a decade or more before they begin to sell or rent fully autonomous cars to the general public.
Even so, the government believes the country will benefit from having related laws put in place in advance.
"It will... enable consumers in the United Kingdom to be amongst the first in the world to reap the rewards that improved transport technology will bring," the bill states.
"Putting the United Kingdom at the forefront of the most modern transport revolution will create new jobs and fuel economic growth around the country."
Other measures outlined by the bill include powers to:
Some businesses may resist being made to invest in the technology at an early stage, but one expert welcomed the fact the government might require them to do so.
"When you've got a big transition to a new technology, the market can take a long time to do what's required," said Prof David Bailey, from Aston Business School.
"So, I think this is about trying to stimulate things more quickly than would happen otherwise."
Insurance cover for self-driving cars must offer protection for both times when the driver is in control and when the vehicle is in charge, according to new proposals from the UK government.