The conductors of the BBC’s orchestras have denounced “irreversible, catastrophically damaging plans” to disband the BBC Singers and make 20% cuts to jobs in the broadcaster’s orchestras in England.

In a letter to the BBC’s director general, Tim Davie, and other senior managers, seen by the Guardian, conductors including Sakari Oramo, Dalia Stasevska and Semyon Bychkov write that they reacted with “disbelief” to Tuesday’s announcement of deep cuts to the BBC’s ensembles.

Referring to the complete disbanding of the BBC Singers, which was founded in 1924, they write that willingness “to consign all this to the dustheap in favour of greater ‘agility’ and ‘flexibility’ displays a shocking disregard not only of how artistic excellence takes root but [of] how the BBC’s great legacy across the arts is viewed and envied around the world. To kill it off takes no time at all, but the ramifications of such shortsightedness are incalculable,” they write. The BBC Singers is the UK’s only full-time choir.

The signatories, who include Ryan Wigglesworth, Ilan Volkov and Alpesh Chauhan, conductors of the BBC Scottish Symphony Orchestra, also take aim at the 20% cuts to salaried jobs to the broadcaster’s three orchestras in England – the BBC Symphony, BBC Concert and the Manchester-based BBC Philharmonic.

“Rewarding the outstanding work of our orchestras with bit-by-bit erosion is equally calamitous,” they write. “Aside from the jargon, to claim that by cutting jobs you are somehow ‘reinforcing the distinctiveness of the BBC’s unique orchestras’ is nonsensical.”

The BBC Singers is a 20-strong choir renowned for its flexibility and skill in tackling the knottiest new music. Since their foundation in 1924, they have been conducted by Igor Stravinsky and Pierre Boulez, sung at the funeral of Diana, Princess of Wales, and premiered works by composers including Benjamin Britten, Gustav Holst and John Tavener. Under their chief conductor, Sofi Jeannin, future plans include a concert of music by the Finnish composer Kaija Saariaho.

Announcing the plans on Tuesday, Charlotte Moore, the BBC’s chief content officer, said: “This new strategy is bold, ambitious, and good for the sector and for audiences who love classical music.”

More than 40,000 signatures had been gathered on Thursday by an online petition calling on the BBC to reconsider the plans.

Separately, the Britten Sinfonia, the east of England-based orchestra, launched an appeal to raise £1m to ensure its survival after it was defunded by Arts Council England last year. The appeal is supported by the composers Steve Reich and Thomas Adès, and the master of the king’s music, Judith Weir.