A saxophone-playing Oxford graduate who lives a "Christ-centred life" has been appointed the first woman bishop in the Church of England.

Downing Street this morning announced that the new Bishop of Stockport will be Rev Libby Lane, currently vicar of St Peter's, Hale, and St Elizabeth's, Ashley in the Chester diocese. She will be consecrated at the end of January.

Because she will not be a diocesan bishop, she will not be among the women bishops that will be fast-tracked into the House of Lords. Bishop of Stockport is a suffragan or assistant bishop post in her current diocese. Southwell and Nottingham is understood to have women on its shortlist for a new diocesan bishop and Oxford is also likely to consider women when the appointments process begins next year.

Libby Lane, who is married to a male priest, George, making them one of the Church's first clerical couples, was among the first women to be ordained as a priest, in 1994. Her pastoral life has been concentrated in the north, in the dioceses of Blackburn, York and Chester. The couple have two adult children.

Although not a "name" outside the Church, she is highly rated within it and came to the attention of senior bishops as one of eight clergy women elected as observers to the House of Bishops.

Speaking at Stockport town hall this morning, she said: "I am grateful for, though somewhat daunted by, the confidence placed in me by the Diocese of Chester. This is unexpected and very exciting. On this historic day as the Church of England announces the first woman nominated to be Bishop, I am very conscious of all those who have gone before me, women and men, who for decades have looked forward to this moment. But most of all I am thankful to God.

"The church faces wonderful opportunities, to proclaim afresh, in this generation, the Good News of Jesus and to build His Kingdom. The Church of England is called to serve all the people of this country, and being present in every community, we communicate our faith best when our lives build up the lives of others, especially the most vulnerable. I am excited by the possibilities and challenges ahead."

The Archbishop of York, Dr John Sentamu, said: "It is with great joy that on January 26, 2015 - the feast of Timothy and Titus, companions of Paul - I will be in York Minster, presiding over the consecration of Rev Libby Lane as Bishop Suffragan of Stockport. Libby brings a wealth of experience in parish ministry, in hospital and FE chaplaincy, in vocations work and the nurture of ordinands. I am delighted that she will exercise her episcopal ministry with joy, prayerfulness, and trust in God.

"When the General Synod rejected the previous proposals in November 2012, Archbishop Desmond Tutu, wrote to 'pour some balm' on my wounded heart. That year, he encouraged me, his province was finally celebrating the election of two women bishops. 'Be comforted', he said, 'it will come.'

"When I wrote to him last weekend to offer my prayers for his battle with prostate cancer, he replied with these words: 'Wonderful that you over there will soon have women bishops. Yippee! I know you have pushed for this for a long time. Yippee again!'

"Praise be to God in the highest heaven, and peace to all in England!"

The Archbishop of Canterbury, Justin Welby, said: "I am absolutely delighted that Libby has been appointed to succeed Bishop Robert Atwell as Bishop of Stockport. Her Christ-centred life, calmness and clear determination to serve the church and the community make her a wonderful choice.

"She will be bishop in a diocese that has been outstanding in its development of people, and she will make a major contribution. She and her family will be in my prayers during the initial excitement, and the pressures of moving."

Atwell is now Bishop of Exeter.

The Bishop of Chester, Dr Peter Forster, a leading evangelical, said: "Libby has had a varied and distinguished ministry, and is currently a first-rate parish priest. She has already demonstrated her ability to contribute nationally through her representative role in the House of Bishops, on behalf of the north-west England dioceses.

"As the first woman bishop in the Church of England she will face many challenges as well as enjoying many opportunities to be an ambassador for Jesus Christ. I have no doubt that she has the gifts and determination to be an outstanding bishop.

"I am delighted at her designation as Bishop of Stockport after a lengthy process of discernment across the Church of England and beyond."

Rev Rosie Harper, chaplain to the Bishop of Buckingham Alan Wilson, wrote on her Facebook wall: "It's happened. The CofE has it's first woman bishop: The Rev Libby Lane, Dean of Women in Ministry, Chester Diocese. Whew! All the very best to her - she'll be under the spotlight! Only took 2,000 years. Roll on the time when other issues of equality are also addressed."

Hilary Cotton, Chair of Women and the Church, said: "This is a great day of rejoicing and a momentous day of change. As 'the first', she will have expectations heaped upon her from all directions. But there will also be an immense wave of goodwill towards her, from within and well beyond the Church of England."

Sally Barnes, also of Watch, said: "It really is a wonderful Christmas gift for the church as well as society generally that is looking for the church to show real value towards women and their/our gifts for the benefit of men and women."

New Wine tweeted: "Delighted to hear the announcement of the new #bishopofstockport Libby Lane! Know our congratulations and prayers."

However, while offering prayers and good wishes to Mrs Lane, the General Synod's Catholic group Catholic group said it regrets "the implications for the wider unity of the worldwide Church."

And coinciding with the announcement, the Society under the patronage of St Wilfred and St Hilda, which is keeping a file of male priests who adhere to the "Catholic" tradition and therefore can be "safely" invited to celebrate Anglican Mass at a parish that opposes women's ordination, announced its process by which priests in sympathy with its objectives can register.

Dr Colin Podmore, chairman of the traditionalist group Forward in Faith, wrote on the website of the Bishop of Beverley, one of the "flying" bishops who looks after parishes opposed to women's ordination: "Catholics believe that both women and men are called to different ministries in the Church. But for theological reasons, we are unable to receive the sacramental ministry of women as priests (presiding at the Eucharist) or bishops (ordaining priests to preside at the Eucharist).

"So when the Church of England has women bishops, how can we know that a priest has been ordained by a bishop whose sacramental ministry of ordination we do recognise? How can we be confident that when he celebrates the Eucharist, we really do receive the sacrament of Our Lord's Body and Blood?

"The need to offer an easy answer to that question of 'sacramental assurance' is one of the reasons why our bishops have formed the society. As it says on the society website, the society provides 'ministry, sacraments and oversight which we can receive with confidence'."

Bishop of Durham Paul Butler said: "This is great news, I am delighted. I want to wish Libby every success, all of our prayers and blessing are with her as she takes on this next stage in her own ministry and that for the Church of England.

"Libby trained for ordination at Cranmer Hall here in Durham and It's great that in this story Durham continues to play an important part in the future direction of the Church."