The move is aimed at deterring speculative account-holders from disrupting the service offered by each society to existing members.
The decision by Derbyshire and Cheshire comes as the tiny National Counties, with just one branch in Epsom, Surrey, also said it was sending back cheques to hundreds of prospective account-holders.
A spokesman for Cheshire, the 19th-largest UK society with 60 branches, said: "Recently, we decided that we would raise the balance needed to open an account to pounds 2,500 for anyone living outside our core Granada TV area, where most of our customers live.
"Local people were still able to open an account for pounds 100. Unfortunately, what we have found is that when you set limits like that it tends to make people think there is something going on and they try even harder to open an account.
"The inflow simply wasn't normal. Rather than raise expectations, we have decided to stop people opening accounts with us," the spokesman added.
A Derbyshire spokesman said his society, the 17th-largest with some 310,000 savers and 50,000 borrowers, was determined to remain mutual.
"We have introduced measures to discourage speculative account openers and allow us to focus on a quality service to our proper customers in our own region," he said.
"A general measure is that we will not open any accounts for people resident outside the society's normal operating area outside the wider Midlands."
The spokesman added that the society's seven city-centre branches would bar new openings other than its Crown account, with a pounds 1,000 minimum, or Capital Bond, with a pounds 15,000 minimum, to anyone other than existing customers or those connected to them.
National Counties' move to send cheques back to prospective members came after it was forced last month to close its doors to all new accounts.
The society, which has 15,000 savers and 5,000 borrowers, had been inundated by a speculative flood of money following reports that if it were taken over, members might be entitled to payments worth up to pounds 4,500.
John Milton, general manager at National Counties, said yesterday: "We have been overwhelmed in recent months by applications for new accounts. Speculative inflows are misplaced and unwelcome.
"The general reaction to our decision has been surprisingly positive."Reuse content