The Bill had set out a framework to allow local government in England to keep all of the £26 billion in business rates it raises locally each year.
But its reintroduction was omitted from the Queen's Speech which instead focused largely on Brexit-related legislation as the UK prepares to leave the European Union.
Of 27 bills contained in the speech, eight relate to Brexit and its impact on immigration, trade and sectors such as agriculture.
The Local Government Association said: "It is hugely concerning that the Government has not reintroduced the Local Government Finance Bill in the Queen's Speech.
It added: "This would close the funding gaps identified below, in children's and adults services."
The association, which represents local authorities, also called for government assurances that billions of pounds in EU regional funding would be protected post-Brexit.
Brexit would have a significant impact on local government, it said, creating challenges that needed to be addressed but also opportunities to do things differently.
"Local government must play a central role in deciding whether to keep, amend or scrap the EU laws which impact on the council services that affect people's day-to-day lives."
Brexit should not simply mean a transfer of powers from Brussels to Westminster, Holyrood, Stormont and Cardiff Bay, said the association.
Instead, it should lead to new legislative freedoms and flexibilities for councils so that local communities and businesses could benefit.
The association added: "We are calling for clear guarantees to protect the £8.4 billion in local regeneration and regional funds.
"This funding is needed to protect local regeneration plans, flagship infrastructure projects, employment and skills schemes and local growth in our communities."
The association said such a commitment would be in line with a government pledge to provide stability to farmers as the UK left the EU, outlined in the government's Agriculture Bill.
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