The legislation which received its first reading in the House of Lords on Friday will look to make all internet service providers introduce filters for adult content and bring about better age verification systems for websites.
Currently only the 4 major ISPs have the filter which means 10% of children across the country don't have indecent material blocked.
The Bill is Baroness Howe's fifth attempt at bringing about a change in the law.
Speaking about today's reading in Parliament, she said: "I am delighted that my new Online Safety Bill has had its First Reading.
"The so-called 'default-on' filtering solution that the Government has championed only applies to 90% of the market leaving many thousands of children beyond it reach.
"Moreover, and of central importance, there is no age-verification process to establish that a person lifting the default filters is 18 years or over before allowing the filters are lifted.
"This is completely unacceptable. Our children deserve better."
She's being supported by the charity CARE, which has campaigned on this issue for many years. CARE's Director of Parliamentary Affairs Dr Dan Boucher said: "CARE wholeheartedly welcomes Baroness Howe's determination to force a change in the law and we will be backing her Bill every step of the way.
"The fact that our online protection provisions may be better than those of many other countries is no reason to hold back when we have the option of significantly further enhancing child safety online."
It's unknown when the Bill will next be debated in the House.
Listen to Dan Boucher speaking to Premier's Hannah Tooley on the News Hour: