The societies, including Alliance & Leicester, yesterday denied they were themselves cashing in on a flood of depositors eager for bumper payouts.
A Nationwide spokesman said: "Since the first reports about National & Provincial's possible takeover by Abbey National, we have seen a wave of speculative account opening.
"Applications to open our CashBuilder account, which has a minimum balance of pounds 100, has been between three and four times its normal rate.
"We feel that people who simply pay in the minimum and have no intention of increasing their balances are forcing up costs for loyal members."
Alliance & Leicester will raise from pounds 100 to pounds 500 the minimum cost of opening an account.
"The increase was in response to steps taken by some of our competitors," a spokeswoman said. "Investors who have considered opening speculative accounts in the past become even more inclined to do so once they hear one society is raising its limits. They then turn their attention to those that have not."
Bristol & West said the possibility of raising the minimum was "under consideration".
However, Britannia and Skipton building societies said they would not raise minimum investment levels.
Skipton yesterday announced pre-tax profits of pounds 12m in the first six months of this year, compared to pounds 7m in the same period of 1994.