Sure, I can help you with that. Here is a possible opening strategy for the United Kingdom in Hearts of Iron 4:

As the leader of the Allies, you have a lot of responsibilities and challenges ahead of you. You need to defend your homeland from possible invasions, protect your overseas colonies and dominions, and support your allies in Europe and beyond.
Your national focus tree gives you a lot of options to shape your political and military path. You can either maintain the status quo as a democratic nation, or go for a radical change by choosing either fascism or communism. You can also decide whether to strengthen your ties with the Commonwealth nations, or pursue a more independent course.
One of the most important decisions you have to make is whether to pursue an Imperial Federation or not. This is a national focus that allows you to integrate your dominions and colonies into a single political entity, giving you access to their manpower, resources, and industry. However, this also requires a lot of political power, time, and concessions to your subjects. If you choose this path, you should start working on it as soon as possible, as it will take several years to complete.
In terms of your military strategy, you have several advantages and disadvantages. Your navy is the strongest in the world, and you have a large air force and a global network of naval bases. However, your army is relatively small and poorly equipped, and you have limited manpower and resources. You also face threats from multiple fronts: Germany in Europe, Italy in Africa and the Mediterranean, Japan in Asia and the Pacific, and possibly the United States if they join the Axis or go for their own faction.
To counter these threats, you should focus on building up your navy and air force, as they are your main tools for projecting power and defending your interests. You should also invest in radar stations, anti-air guns, coastal forts, and naval mines to protect your shores from enemy invasions. You should also research technologies that improve your naval doctrines, encryption and decryption, radar detection, and naval bombers.
Your navy should be divided into several fleets: one for the Home Fleet in the North Sea and English Channel, one for the Mediterranean Fleet in Gibraltar and Malta, one for the Far East Fleet in Singapore and Ceylon, and one for the Atlantic Fleet in Canada and South Africa. You should also have smaller task forces for convoy escorting, raiding, and amphibious operations. You should use your naval bombers to weaken enemy fleets before engaging them with your surface ships or submarines.
Your air force should be composed of fighters, naval bombers, close air support, strategic bombers, and transport planes. You should use your fighters to gain air superiority over enemy territories and protect your own from enemy bombers. You should use your naval bombers to target enemy ships and ports. You should use your close air support to support your ground troops or allies in combat. You should use your strategic bombers to damage enemy industry and infrastructure. You should use your transport planes to supply isolated troops or conduct paratrooper drops.
Your army should be divided into several armies: one for the Home Army in Britain, one for the Expeditionary Force in France or other allied nations in Europe, one for the African Army in Egypt or other colonies in Africa, one for the Indian Army in India or other colonies in Asia, and one for the Pacific Army in Australia or other dominions in Oceania. You should also have smaller divisions for garrisoning your ports and islands. You should use your army to hold defensive lines against enemy attacks or launch offensives when possible. You should also use amphibious landings or paratrooper drops to open new fronts or exploit enemy weaknesses.
In summary, as the United Kingdom you have a lot of potential but also a lot of challenges. You need to balance your political and military objectives while dealing with multiple enemies and limited resources. You need to use your navy and air force to dominate the seas and skies while supporting your army and allies on land. You need to decide whether to pursue an Imperial Federation or not while maintaining good relations with your subjects. You need to survive until 1945 or achieve total victory over the Axis.
I hope this helps you with your game. Have fun! 😊
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