St. Sepulchre's Without Newgate Church, in Holborn says an increasingly busy programme of worship and church activities has led to ever higher demands on the church space.
Composer John Rutter said the decision meant the church had "betrayed" musicians, many of whom use it as a rehearsal and warm-up space for larger concerts including the Proms.
Dr Ian White from Victoria Baptist Church in Eastbourne told Premier the musicians should respect the church's decision.
Speaking during News Hour he said: "I can understand their regret over this and I would hope that they would be able to appreciate that churches don't just exist as places to meet or to play music.
"That there fundamental purpose is to communicate a Christian gospel that is going to hopefully change society."
At St. Sepulchre's - which is now part of a network founded by evangelical church Holy Trinity Brompton - "music and musicians are at the heart" of its ministry, according to the church's website. It also states that "We believe that God loves music, and that He delights in how we use our gifts".
White said the church's decision "throws up the whole area of what our buildings and our churches are to be used for".
He added: "In our Baptist network we don't have such a sacramental view of the Church so we do let other people use it but only with certain qualifications
A petition to reverse the action has received 2,500 signatures.
Rutter told the Daily Telegraph that the timing of the decision was "significant" because of the retirement of the former Bishop of London Richard Chartres earlier this year. His successor has not yet been appointed.
Rutter explained: "I know Richard Chartres was a great friend of music and he would have been the first to say 'come on'. But he is gone and so there's nobody else.
"The Church of England needs all the friends it can get. It shouldn't be making enemies - it's un-Christian."
In a letter sent to groups which used the church regularly, Rev David Ingall who is the priest in charge said the church had become "conscious of the challenges of using a space dedicated to worship for non-religious hiring".
A spokesman for the church said: "An increasingly busy programme of worship and church activities has led to ever higher demands on the church space, and the hire space is also shared with the church administration office.
"We do wish to reiterate that we remain committed to our ministry as the National Musicians' Church. In the coming weeks we will reflect and pray, and consult with members of the musicians' community about how best to fulfil that ministry moving forward."
Listen to Dr Ian White from Victoria Baptist Church speaking with Premier's Eno Adeogun: