Happy Dad If you go back to mid October on this thread you will see that links were posted as the background to the school bid was researched, including to sermons etc.
I don't agree that traditional mainstream christian views on marriage would be consistent with Christian Evangelical beliefs eg the Complementarianism proselytised by the International Outreach Director of the American Evangelical Council for Womanhood and Manhood (who spent a week at Fulham Boys' School) as set out in his book. [http://www.gavinpeacock.net/the-grand-design]
Traditional girls' CofE schools have never in my lifetime offered that as the model for their pupil's futures but rather have always empowered girls to aspire to success in whatever field they chose. Looking at the website of Lady Margaret School (which is near Fulham Boys' School and has long been very popular and perhaps explains the demand for a boys faith school in the area) I see no suggestion that the school's strategy for female empowerment is any different to the one my own CofE school had in what my children refer to as Victorian times 
. It wasn't but actually that was actually the ethos many of those schools had had since first established in Victorian / Edwardian times. Whilst I agree the same cannot be said for views on same sex marriage actually the struggle within the CofE on the issue (and on women priests) has arisen just as much as a result of opposition from the Evangelical constituency.
I think you need to disentangle traditional from Conservative Evangelical/ Fundamentalist. Conservative Evangelicals believe in a literal translation of the bible so you cannot separate creationism from their belief that God offered Adam and Eve as the model for mankind as set out in the bible and complementarianism as a celebration of Gods creation (as set out in the "Grand Design" bumf in the link above). Their beliefs are also most definitely anti abortion.
If you look at the Headmasters and Chaplains blogs Mr Ebenezer, the Headmaster, quite specifically wants all these issues to be discussed openly by the boys at Fulham Boys School. Now obviously we want our children to discuss all issues of religious belief but according to the DofE's "British" values this should be done in an atmosphere that promotes equality, and the theory of creationism definitely should not be given equivalence to the theory of Evolution which Mr Ebenezer proposes in a recent blog. Implicit in that is that it should be taught in the Science curriculum but it is definitely not part of the national curriculum. I just don't see how Mr Ebenezer's robust views are consistent with British values (unless of course white fundamentalism is somehow exempt ). I think the school's proposal should have been honest about the background of the proposers and the agenda they want aired at the school (as outlined in the headmasters blogs for FBS) so parents can decide if that is what they want for their children...
As to International links the international nature of christian evangelical networks both theological and financial, particularly in relation to the US, manifest themselves in lots of ways you can track down online. There was the week long visit of the International Outreach Officer of an American Evangelical Organisation to Fulham Boys' School already mentioned. Mr Budds has written up his Adam and Eve work for a magazine called Evolution News [https://evolutionnews.org/2017/10/does-science-rule-out-a-first-human-pair-geneticist-richard-buggs-says-no/] which is based in Seattle and describes itself as "Evolution News & Science Today is a great tool for countering pro-Darwin propaganda. And for opening minds.
The spirit of the age says mindless evolution turned microbes into men. It whispers this “fact” in countless classrooms, textbooks, and academic articles. The media then recycles the message in a steady flood of approving stories.
The writers at Evolution News are our first responders. They wade into this flood of pro-Darwin misinformation and rescue the truth with evidence and logic. In 2017, they published over 750 articles dealing with new scientific findings and philosophical arguments. They provided ammunition to defend the case for intelligent design."
The Duke street Church has £6m in asetts and recieves over £0.5m in donations each year including donations to international evangelical organisations. apps.charitycommission.gov.uk/Accounts/Ends92/0001134492_AC_20171231_E_C.PDF
When Mr Buggs was actively eliciting support for the school he had several challenges both semi publicly in the Next Door forum and privately but did not take any of the opportunities to uncloak and open up on the proposed schools ethos in relation to eg homosexuality. The proposal has now gone to the DofE and that decision making process is opaque, aside from the Council having an advisory role. It does seem as if it is unlikely they would change the decision on this site though, and there is no need or site for another secondary school so it should not be a worry that they will get to open here (especially as local governing bodies and the Council do now know the background), cloaking the proposal as a local one might actually be an own goal that prevents them from being approved to open elsewhere........