Here's a possible scenario merging a few of these PODs.
1957: after Sputnik, the British government listen this guy from the RAE and Black Prince is a go.
https://en.wikipedia.org/wiki/Desmond_King-Hele
First flight planned for 1960- something. Out of Black Knight the british creates an optimal second stage for Blue Streak : 2 meters diameter and 14000 kg heavy.
1960, April: Blue Streak canned, Black Prince threatened. The British Government decides to hire the French as partner.
1961: the French agree, for a solid-fuel third stage. They add that a switch to LOX-LH2 should be done ASAP.
Thinking about it.
If the british decide to make an enlarged Black Knight early (Probably 54 to 72 in. - 1.37 to 1.83m - diameter instead of 2m, tbh), then they would naturally look into it as alternatives to Blue streak (1960) and/or Skybolt (1962) as IRBM after their respective cancellations. Whether it becomes an operational vehicle is largely up to Anglo-American relations, but there would probably be substantial work on turning it into an IRBM - including guidance,which would be much improved, and there would probably be military funding, keeping the Second stage of this "black prince", relatively afloat after the Blue Streak IRBM cancellation.
In turn it would affect Franco-British negociations, The french were rather relunctant to commit to a Franco-English BS-derived launcher initially, especially for 50/50 of the funding with minimal french participation, 25% of the cost was the maximum French counter-proposal through the period from what I've read, and they always wanted more continental european involvement to lower cost and British influence.
However the French were also quite interested in guidance and reentry technology, IRL it was in vain, given the Anglo-American origins of Blue Streak, but a Black Knight-derived IRBM (as an alternative to BS/Skybolt) would be fully british and still in study/development by that point , and the French side would at least *think* that there would be more potential for technology transfer.
We know that Force de frappe cooperation was of potential interest to de Gaulle, before (May-June 62) the Nassau agreement, him and his government had proposed to McMillian an Anglo-French deterrent, and some of the litterature suggests this may have been enough to make him accept the British entry into the EEC. This doesn't go nearly as far, but the prospect of technology transfer as well as french involvement adjacent to the British IRBM industry may be enough to persuade the French to better fund this Anglo-French launcher, maybe not enough for a 50/50 collaboration, but maybe enough to offset the lesser French industrial involvement (3rd stage vs 2nd stage) and lack of other continental european partners.
For reference (exchange rate according to
https://fx.sauder.ubc.ca/etc/GBPpages.pdf), from H. Moulin and C.N.H's books
| All in Millions | New Francs | Pound | Dollars ≃ MAU |
| Fall 1960 Franco-English Proposal (British Estimate) | 719 | 52 | 145.6 |
| 50/50 British demands 1960 | 359.5 | 26 | 72.8 |
| 1961 British Estimate | 967 | 70 | 196 |
| 1961 50/50 British demands (pre-Strasbourg) | 484 | 35 | 98 |
| Mid-1961 French ELDO Budget proposal (20%) | 193,5 | 14 | 39.2 |
| Mid-1961 UK ELDO Budget Propsal (25%) | 242 | 17,5 | 49 |
| 1st ELDO Preparatory group French budget agreement (23.93%) | 231.5 | 16.75 | 46.9 |
| 1st ELDO Preparatory group UK budget agreement (38.79%) | 375.3 | 27.15 | 76.03 |
| November 1961, maximum French backup plan if Italy doesn't participate (26.32%)* | 254,5 | 18.4 | 51.5 |
| | | |
| CRUSADE + 54 in. Black Knight estimate 1964 (Ministry of Aviation) | 66.35 | 4.8 | 13.55 |
| Black Arrow dev cost (1964 estimate) | 138.24 | 10 | 28 |
| | | |
*Auger plan 1b), 23 millions New Francs more to 1965 included than the alternative.
