Evangelical bishops in the Church of England have offered a hand of friendship to GAFCON – the international Anglican grouping emerging as a potential future alternative to the Anglican Communion.

In an unexpected overture, 13 bishops have written a letter declaring that it is 'really important' for them 'to stay in good relationship' with their 'orthodox Anglican brothers and sisters' in GAFCON, and say they hope their initiative in reaching out 'can mark the beginning of better communication and liaison between us'.

At the same time, the bishops make it clear they have no intention of leaving the Church of England at the moment, stating: 'We hope that you will understand our continuing commitment to [it], which we see as privilege, gift and calling, and that you will hear our request to work together closely as partners in the Gospel as we journey into God's future.'

The olive branch to GAFCON comes just days after an earlier letter from evangelical bishops warning the Church of England not to liberalise its sexual ethics. While there is some overlap in signatories, the list of those signing is not identical.

The bishops behind this second letter say they are writing in response to GAFCON's 2018 assembly in Jerusalem, and the 'Letter to the Churches' which was produced there. They express agreement with GAFCON's view of the crisis in Anglicanism: 'The analysis of the current tragic situation in the Anglican Communion which is set out [in GAFCON's letter]... is one which resonates with our experience as Bishops in the Church of England... We cannot disagree with the GAFCON diagnosis concerning the tear in the fabric of the Communion.'

And referring to GAFCON's call for liberal provinces not to be invited to the next global conference of bishops at Lambeth in 2020, the bishops say 'representations will need to be made' to Justin Welby 'by all orthodox Anglicans, in order to indicate the strength of feeling on this issue'. They also 'resonate' with GAFCON's wish for its new conservative Anglican provinces in North America and Brazil to be invited.

The bishops say they see it as their 'present calling' to 'remain committed to the Church of England'. But they also admit: 'There may come a time when the Church of England... departs from the biblical and apostolic Faith – and this might occur for any number of reasons.' At the moment, however, they say 'the core doctrine of the Church of England remains unchanged'.

They add: 'There is some popular misrepresentation of the current House of Bishops which alleges that we are heterodox; we recognise the fears, but our personal conversations and experience lead us to the conclusion that [this] perception is far from the normative reality.'

The letter goes on to 'recognise that the GAFCON movement is something that has united Anglican Churches across the world who are looking for a different shape for a global Communion', but adds: 'We regret that no recognition is given in the letter to those who in good conscience believe it is right to stay within their current Anglican structure.'

Archbishop Foley Beach, Primate of ACNA and Chairman-designate of GAFCON, is currently on a tour of the UK. It is not clear whether he or the letter-writers have been in touch with one another yet to meet face to face. The letter from the bishops says: 'We would welcome the opportunity to engage more fully in conversations with GAFCON UK about its polity, how it sees itself in relation to the Church of England, and about its missional strategy and purpose.'

The bishops say they were grateful for the invitation to attend GAFCON 2018. But they state that a problem in doing so was the requirement to sign an extra declaration of faith in addition to that which they had already made for the Church of England. 'Perhaps,' they say, 'there is room for some accommodation on this issue for those of us who would like to attend future GAFCON events'. They also ask for 'liaison between us' as GAFCON's networks are developed in England.

Signatories to both letters this week are the Bishops of Peterborough, Willesden, Durham, Blackburn, Ludlow, Plymouth and Carlisle, and Rt Rev Mark Rylands, formerly Bishop of Shrewsbury and now an assistance bishop in the Diocese of Exeter. Signatories to the first letter but not the second are the Bishops of Birkenhead, Maidstone, Lancaster, and the retired Bishop of Shrewsbury; signatories to the second letter but not the first are the Bishops of Winchester, Lewes, Guildford, Basingstoke, and Southwell & Nottingham.

One reason for some of the difference is that the signatories of this new letter do not include those bishops who attended GAFCON in Jerusalem – it comes specifically from evangelical bishops who did not attend. The full text of the letter is being posted on the website of the Church of England Evangelical Council.

David Baker is a former daily newspaper journalist now working as an Anglican minister in Sussex, England. Find him on Twitter @Baker_David_A