The Church of England is on course to give its final approval to female bishops next year after its General Synod voted in favour of new proposals to bring women into the episcopate, raising hopes of an end to the damaging and frequently bitter 20-year standoff between modernisers and traditionalists.

On the third and final day of its meeting in London, the synod voted in favour of the new plans by an overwhelming majority of 378 to eight, with 25 abstentions.

Proposing the new draft legislation, the bishop of Rochester, James Langstaff, recognised that the synod had been given a "second bite of the cherry" but said that it had come a long way since last November, when the last moves to introduce female bishops fell.

He urged the synod to vote "as positively as it is able" for the proposals, adding: "People may have quibbles about various words and phrases within this statement of guiding principles, but I would ask you to remember that these are guiding principles, not holy writ nor a creedal statement.

Although the first speech from the floor noted that "history makes us naturally cautious about optimists who wave documents that offer peace in our time" – and a later one described the previous failure as "missionally disastrous" – it soon became apparent that a consensus had been reached and that many key former opponents from the conservative evangelical and Anglo-Catholic wings of the synod had come to accept the new plans.

The Rev Rod Thomas, chair of the conservative evangelical group Reform, conceded that his decision to vote against the previous draft legislation had been "a cause of shock, of bewilderment, of anger and of grief" to many.

Thomas said that although he still had reservations over some aspects of the new package, he intended to support it even if he found himself unable to vote for final approval for female bishops next year.

"In the spirit of agreement we have reached, in the spirit of wanting to achieve agreement I will vote for it," he said. "And even if at the end of the day I am unable to join the majority at synod – who I confidently expect to approve this by the required majorities – even if I am not able to join you, I shall rejoice in the measure of agreement that we have been able to reach."

However, Reform's director, Susie Leafe, said she simply could not bring herself to follow suit.

"How I wish that I, too, could stand here and say that all was well," she said. "But I can't … We claim that this package is designed to enable all to flourish yet I and my church can only flourish once we've denied our theological convictions and accepted a woman as our chief pastor."

Prominent Anglo-Catholics who had opposed the previous legislation also announced they would back it.

The Rev Paul Benfield – who sat on the steering committee that yielded the new proposals but had previously abstained from commending its recommendation to the synod – supported the new plans despite concerns over issues of jurisdiction.

"I think this is a workable way forward and so I shall vote for this motion and I shall vote in the next debate to put this legislation for revision in full synod," he said. "I urge you all to do the same."

Christina Rees, a member of the archbishops' council and veteran campaigner for female bishops, said she could scarcely believe how far the synod had come in 12 months.

"If anyone had told me that one year on from last November we would be where we are, I would have said: 'That's impossible,'" she said. "But by the grace of God it has been possible and here we are. And I believe that what we are considering now is better than what we had last year and I also believe that we are better as a synod."

Despite the outbreak of peace, the archbishop of York was careful to sound a note of caution and warn against premature rejoicing.

"Your generous magnanimity is palpable," said John Sentamu. "However, may I bid us all that we should not open champagne bottles – or whatever drink we're going to celebrate with – because we need to continue to walk together till the end. As Francis Drake said: 'There must be a beginning of any great matter, but the continuing unto the end until it be thoroughly finished yields the true glory.' And until we all get together we need still to stick together and stay in the same place."

Speaking after the ballot, the bishop of Rochester, who chaired the steering committee , said that he had been encouraged by the "hugely positive" vote, but stressed that there was no room for complacency.

"There is still a lot of work to be done and people will have voted in favour of this because it's about continuing the process [but they] may or may not vote in favour of the package at the end of the day and that's a reality," he said. "So it's not over. I suspect I've got a job to do for the next few months."

The bishop said much of the credit for the result belonged to the archbishop of Canterbury, Justin Welby, who has worked as a mediator and peace negotiator in some of the most dangerous places in the world.

"He is something of an advocate of conciliatory processes," said Langstaff. "Without those three facilitators working with us through the steering committee, I suspect we would not have got to where we've got to. And so I think Archbishop Justin's influence in that regard has been a significant mover-on of the process."

Wednesday's vote comes a year to the day after the church was plunged into crisis when the last attempt to introduce female bishops was defeated by just six votes.

The narrow defeat put the C of E under huge public and political pressure: its failure to resolve the issue was described by the church's most senior civil servant as a train crash, while David Cameron warned that the church needed "to get on with it".

Langstaff denied that the church had felt under political pressure to resolve the issue, saying: "We had to do this anyway and it's far better that we should have done it ourselves than had somebody else do it for us or put pressure on us and we have done it."

Asked where the church was after last year's "train crash", he offered a long metaphor that almost collapsed under the weight of its symbolic freight.

"The train is on the tracks," he said. "The train is moving forwards and we know there are some stations we've got to pass through along the way, but we can begin to see the end of this particular journey."

The synod had been asked to give first approval to plans produced by a steering committee of 15 that included five synod members who voted against last November's draft legislation.

Among the recommendations is the creation of an ombudsman who would rule on disputes over arrangements once female bishops are in place.

Under the plans, female bishops would be introduced with a house of bishops "declaration" setting out guidance for parishes where congregations reject female ministry.

The ombudsman – appointed by the archbishops and with the backing of lay and clergy representatives in the General Synod – would be given power to investigate where complaints were made about arrangements.

At the last meeting of General Synod in July, the church was told that if it did not move on female bishops, parliament would step in.

Sir Tony Baldry, who speaks on the church's behalf in the House of Commons, told the York meeting: "If we haven't got this sorted by 2015 then I cannot account for the law of unintended consequences at Westminster as to the creative ability of colleagues on both sides of the house of getting involved in this.

"I put it no further than this: a number of senior privy counsellors on both sides of the house are already putting their minds to how do they sort this if General Synod doesn't."

The synod, he said, needed to remember that it did not exist in a bubble: "The world is looking at us – and not least parliament."

The steering committee, however, appeared to have paid dividends and narrowed the differences on the issue. Those in favour of bringing women into the episcopate had been quietly confident the latest set of proposals would win favour at the synod and believed that some of the Anglo-Catholics and conservative evangelicals who opposed the previous attempt had become more open to finding a solution.

Campaigners were also encouraged by a new, more collegiate spirit within the synod and last week's statement from the Anglo-Catholic group Forward in Faith urging its members to back the new plans.

"Though these proposals are still far from what we have long said would be ideal, we believe that they may have the potential to provide workable arrangements for the future," said its chair, the Right Rev Jonathan Baker, bishop of Fulham.

While acknowledging that some of the group's members would ultimately find themselves unable to vote in favour of female bishops should the synod take a final vote on the matter in a year's time, he said the proposals nonetheless held out "the possibility of bringing to a conclusion a process that for too long has been a distraction from the church's mission".