MILAN (Reuters) - Italian lawmakers have put forward a proposal for free Wi-Fi in thousands of public places to bridge a gap with other European countries in broadband penetration, e-government and other digital services that is dragging on the economy.

Under the plan, large shops, taxis, airports, law courts and other public places would have to set up an Internet connection and offer no-password wireless access free.

"We are really badly placed when it comes to Internet access," Sergio Boccadutri, a member of the ruling Democratic Party and sponsor of the proposal, said.

"Free Wi-Fi would have a big cultural impact and help the economy recover, starting from industries such as tourism."

The proposal, filed this week, has the support of more than 100 members of parliament and would earmark 5 million euros ($6.3 million) over three years as a contribution to buying equipment. The proposers aim to bring the bill before parliament by mid-2015.

According to a report this month by Milan's Politecnico university, high prices and the lack of access infrastructure are the main barriers to households using the Internet.

Data in the study showed penetration of broadband services with a speed exceeding 30 Megabits per second in Italy is lower than 1 percent, well below the European average of 6 percent.

(Reporting by Danilo Masoni; Editing by Louise Ireland)