Senior clergy members say they were not consulted over provisions for a second national lockdown and will write to the Government to question why "certain exemptions" have not been made.
The Archbishops of Canterbury and York, and the Bishop of London say they will also emphasise the "critical role" that churches play in the community.
In a letter written to the clergy of the Church of England (CoE), Justin Welby, Stephen Cottrell and Sarah Mullally praised the "energy, hard work and creativity" of members which had allowed worship to continue during the pandemic.
"We are grateful that the new guidelines being introduced on Thursday not only allow churches to remain open for private prayer but also enable online worship to be broadcast from the church building," they said.
"We were cautious about these issues during the first lockdown - perhaps overly so - but in this second lockdown we want to encourage church buildings to remain open for private prayer wherever possible."
The bishops said that more resources and training would be given to church leaders to enable them to conduct services online.
But they added that the use of sacraments was an integral part of physical services and should not be viewed as an "optional extra" by the Government.
"Worship online still means that the people of God do not have access to the sacraments which are so central to our life in Christ," they said.
"This is a huge loss and since we were not consulted about the lockdown provisions, we fully intend to speak with Government about why certain exemptions are made and not others, emphasising the critical role that churches play in every community.
"The sacramental life of the church cannot be seen as an optional extra.
"Nor can we separate out our worship from our service, it is always both and not either or.
"Nevertheless, we will of course abide by the law and ask you to do the same.
"We must do all that we can to keep our communities safe and to enable the NHS to manage this crisis."