Most of these programs were canceled, especially after the 1958 United Kingdom-United States Mutual Defense Agreement. This offers some insight into what direction an independent or Franco-British military nuclear program might have gone. Information from here. Blue Badger/Blue Bunny/Blue Hare/Brown Bunny/Violet Mist: A truck mounted nuclear weapon, intended to delay Soviet armored advances through the FRG. Estimated 20 to 100 kiloton warhead. Blue Bishop/Green Janet: A program to develop 2 MW air mobile nuclear reactor for powering military bases and a 5 MW sealift capable portable nuclear reactor for use in areas with undeveloped or damaged civilian power grids. Blue Boar: A TV guided nuclear bomb project, canceled because the resulting weapon was too heavy for use by naval aviation and because much of the Soviet Union was subject to periods of prolonged cloud cover. Blue Danube: A 20 kiloton plutonium bomb, the first operational British nuclear weapon. Blue Fox: A 1955 proposal for a lightweight 6.5 kiloton warhead for use by the Bloodhound air defense missile. Blue Peacock: A 20 kiloton nuclear landmine. Blue Steel and Blue Steel Mk. II: Air launched nuclear armed missiles. Blue Streak: A British medium range ballistic missile. The United Kingdom became the first country to develop missile silo technology as part of this project. Blue Water: A nuclear armed tactical missile for the British Army. The project was canceled and the British Army purchased Honest John rockets from the United States instead. Green Bamboo: 500 kiloton boosted fission gravity bomb. Green Cheese/Yellow Sand: A radar guided missile for the Blackburn Buccaneer based on the Blue Boar design. Green Flash: Green Cheese replacement. Green Granite: 1 megaton to 3 megaton thermonuclear gravity bomb designs. Green Grass: 500 kiloton fission warhead. Indigo Hammer: 6.5 kiloton thermonuclear warhead for the Bloodhound Mk. III. Orange Herald: 720 kiloton boosted fission variant of Green Grass. Purple Granite: Two stage 200 kiloton thermonuclear weapon. Based on Green Granite. Purple Passion: 0.01 to 0.1 kiloton nuclear demolition warhead. Likely similar in role to the United States Special Atomic Demolition Munition. Red Beard: Tactical nuclear bomb for the Royal Air Force. Red Snow: 1 megaton warhead for Yellow Sun and Blue Streak. Based on United States Mk. 28 warhead design. Violet Club: 500 kiloton thermonuclear weapon intended as an interim weapon prior to the introduction of Yellow Sun. Violet Vision: 15-25 kiloton modified Red Beard warhead for use on British Corporal missiles. Yellow Anvil: Atomic artillery shell for the British Army. Yellow Sun: Boosted fission (Stage 1) and thermonuclear (Stage 2) gravity bombs for use by the V-Bomber force. Yield of 400 kilotons to 1 megaton.
If those are implemented the British and French nuclear forces would be much larger than they where in OTL.
If you look at this 2015 fissile material report you can see how the British and French nuclear programs have produced vast quantities of plutonium. This is because the early programs were built around Magnox and UNGG type reactors designed to produce large amounts of plutonium, and also because the British and French reprocess their civilian fuel. Countries generally keep their civilian and military materials separate, especially because Article III of the Nuclear Nonproliferation Treaty requires it for all signatories, including nuclear weapons states, but that wasn't a hard rule in the 1950s and 1960s. For example, the Calder Hall and Chapelcross Magnox reactors were owned directly by the United Kingdom Atomic Energy Authority and while they produced civilian power, they also ran on fuel cycles optimized for plutonium production (instead of power production) full time until 1964, the occasionally produced military plutonium until 1995. Later Magnox stations were owned by the Central Electricity Generating Board, but Hinkley Point A and the next two stations of the Magnox program were built with modifications allowing them to be used for military plutonium production.
The United Kingdom briefly pursued "megaton" class fission bombs due to difficulties developing thermonuclear devices. Those are weight, inefficient materials usage, safety and readiness concerns due to the large number of critical masses in a single core and the safeguards that must be employed to prevent a criticality accident or even a nuclear fizzle partial detonation. More information on such fission bombs here.