The National Union of Journalists, Bectu and Unite wrote to the BBC's director of business operations Lucy Adams asking for a pay increase of inflation plus 2% with a minimum increase of £400 to be applied to all eligible staff.
However, Adams called the unions' demands unrealistic in the current economic climate, and said that the BBC "won't be able to change this through negotiation". The offer of a 1% pay increase is said to be "final" from the corporation.
Union officials now intend to consult branches and chapels throughout the BBC to gauge the feeling among staff about the pay offer. They said that by August this year, the pay anniversary date, the BBC's meridian pay rate will have dropped 8% behind inflation over the past eight years.
NUJ general secretary Michelle Stanistreet said: "Given all the sacrifices that BBC staff have made in the last year it is insulting to be offered a rise that falls 3% short of the current inflation figure."
Gerry Morrissey, BECTU general secretary and lead negotiator, said: "This is a clear attempt by the BBC to make staff pay for last year's bungled negotiations over the future level of the licence fee.
"We cannot accept a further cut in living standards for members, when the BBC has already taken tens of millions of pounds out of staffing costs by cutting 4,000 jobs, and watering down pension rights."
The unions said that they agreed to co-operate with the BBC last year in a "major overhaul" of the terms and conditions for staff with a view to making "significant savings" under the current budget squeeze in the corporation's new licence fee settlement.
However, they are "angry" that BBC management "appears to have taken no account of this major concession when budgeting for this year's pay increase".
Unions had called for a minimum increase of £1,000 to help BBC staff at the bottom of the pay scale who are struggling to make ends meet as inflation continues to rise, but BBC management only offered a £400 minimum rise.
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