Legislation which allows councils to hold remote meetings expires on May 7 with the government saying it will not be extending the law before that date.
It means that councils, which have been allowed to conduct meetings online to reduce the risk of spreading coronavirus, will now have to make arrangements to hold physical meetings again after that date.
Shrewsbury Town Council's Clerk, Helen Ball, said that the remote meetings had led to a greater level of interest from the public.
She said that the council also faces difficulties in finding a venue to hold meetings safely.
She said: "It is quite disappointing that Government is reluctant to allow permanent regulations for the management of council meetings.
"Back in May last year we all started meeting remotely and they were hard to get used to, but councillors and officers did adapt really well.
"We in turn had greater councillor engagement, more members of the public logging onto the live meetings, more public questions that were asked, more press engagement and ultimately more press coverage about our activity.
"Councillors hoped to see the ability to have a hybrid system whereby full council meetings and annual council could be held physically where the standing committees could be held remotely."
She added: "Currently we are struggling to find a venue that can host town council meetings safely in accordance with the revised regulations, particularly as both Shirehall and Guildhall are not accepting any external bookings."
Earlier this month Shropshire Council's leader, Councillor Peter Nutting, who also sits on Shrewsbury Town Council, said he wanted to see the capacity for remote meetings retained.
Speaking at this month's cabinet meeting, he said: “I’m hoping everyone will agree that either I or the officers put together serious representations to the Government about the need for a change in their attitude.
“I think the answer will by hybrid meetings. We do need to make sure the technology exists, but Shropshire Council can provide that for parish councils if necessary.”
The government has asked town councils for evidence so it can make a decision on whether to bring back legislation that would allow remote meetings in the future.
In a letter outlining that the current legislation would not be extended, Luke Hall MP,Minister of State for Regional Growth and Local Government, said: "I am launching a call for evidence on the use of current arrangements and to gather views on the question of whether there should be permanent arrangements and if so, for which meetings.
"There are many issues to consider and opinions on the detailed questions vary considerably. This will establish a clearer evidence base of opinion and enable all the areas to be considered before further decisions are made. The Government will consider all responses carefully before deciding to how to proceed on this issue."
Shrewsbury Town Council’s Finance & General Purpose Committee will discuss the matter at its next meeting on April 12.