Coventry Building Society barred some account openings altogether after being similarly inundated. Both societies have declared their commitment to mutuality.
At Nationwide, 25,000 new accounts were opened in a single day last week, with some branches running out of passbooks as they tried to cope with a flood of applications from so-called "carpet-baggers".
The openings come as Nationwide fights off a bid by five rebel members, campaigning under the banner Members for Conversion, to win seats on the society's board in this month's election. If the rebels were to win, or to do well in the election, they would claim this reflected a mandate for demutualisation.
The Building Societies Commission, the industry's watchdog, denied suggestions yesterday that it was seeking to bar the five candidates on the grounds of inexperience. A spokesman said that, as with all successful candidates, their suitability would be assessed after the election.
Nationwide claimed yesterday that a large number of new openings were not from windfall speculators but from genuine savers attracted to its highly competitive rates.
"A large proportion of the openings is not speculative in that sense. For example, what we are seeing is the average balance is pounds 10,000 compared with the pounds 500 minimum. A lot of that comes from demutualising societies."
Nationwide is increasing the minimum balance on some accounts to forestall carpetbaggers. These include the Capital Builder account, whose opening balance stood at pounds 1,000, was dropped to pounds 500 in April but has been raised back to pounds 1,000. Invest Direct, another account, has gone from pounds 500 to pounds 2,000.
Coventry said it had been pushed into halting new openings of MoneyMaker and Bonus savings accounts.
Other accounts would only be available to customers living within certain Midlands postcodes.