Industrialization is the core mechanic of Vicky2, similar to how Trade is core to EUIV though even more intense. There are a lot of mechanics at work when it comes to industrialization. I'll try to cover the basics here but I'll probably forget a few things as it's a very complex subject like you mentioned.
Firstly, industry relies on raw materials, which are gained from RGOs. If you don't have access to the necessary raw materials your factories won't be able to make their products and will usually fail. This leads us to the subject of the market and to a lesser extent population types(pops in short) in Vicky2. The market is divided into 2 spheres: local and global. The local sphere is your own nation as well as anybody that shares a sphere with it, in your example you're playing the UK so your local market is your own territory as well as those of all your spherelings. If you were to place as Greece for example who is sphered by the UK at the start than the local market would be the same, however the priority is always with the UK as it's the sphere leader. The global market is everything that falls outside the realm of your local market. Your pops and factories first attempt to buy their needs from the local market and than attempt to buy the rest from the global market. Selling into the global market is even, which means that when X nation buys Y product from the global market, Y product is being sold to it evenly between all the nations producing it. However buying from the global market is prioritized based on prestige. The most prestigious nation gets to buy its pops'+factories' needs from the global market first, than the 2nd most prestigious, etc. That's why most uncivs and other low prestige nations can't support even infantry armies nor industrialize, they simply can't buy their needs from the global market as by the time it's their turn to buy the global market is already empty.
All pops in Vicky2 have money and use it to buy their needs. Different pop types have different needs, also needs are divided in 3 categories: life needs, basic needs, luxury needs, if you're familiar with Maslow's hierarchy of needs than it should be simple to understand. When you click on your budget than hover over a certain pop type you can see how many of them get their life, basic and luxury needs. If you hover over the different needs in the pie chart than you'll see what those needs are for each class(poor, middle and rich). Pops also evolve and devolve over time. For example farmers can evolve into craftsmen, both in the same class but craftsmen generally being richer than farmers but also evolve into the middle class(bureaucrats, clerks and clergymen), likewise with the other classes. The formula is a well hidden secret but we do know that it is affected by education and you can further influence it by setting national focus in certain provinces to encourage your pops to evolve into a certain class. For example to maximize your research you want 2% clergymen in each of your provinces, so setting your national focus in a certain province to clergymen will induce your pops to become clergymen more than other professions. It won't be instant nor absolute, just another rather big factor in the evolution and devolution of pops.
Factories specifically require craftsmen to work in them. They also benefit from having Clerks(improves factory output) and Capitalists(improves factory input). This leads us to factory efficiency, there are 3 categories that make your factories more profitable: input, output and throughput. Better input means it requires less raw materials to make the same products, so if for example it takes 1 unit of coal to produce 1 unit of cement if you increase your input by 1% than it will now take 0.9 units of coal to produce the same 1 unit of cement. Better output means that for the same amount of raw materials you make more products, so as with the above example, if you increase your output by 1% than the same 1 unit of coal will now produce 1.1 units of cement. Throughput increases the overall efficiency of your factory, so as with the above example if you improve throughput by 1% than it will take 1.1 units of coal to produce 1.1 units of cement.
Throughput is clearly the worst bonus as it doesn't improve your resource efficiency at all, however throughput is generally gained at larger quantities than input and output bonuses and it still helps your factories to produce more goods and therefore generate more profits. The other ways to increase input, output and throughput other than pop types is technology and inventions, check the different technologies and inventions(in the industry tree for throughput, commerce for input and output) to see how you can improve your factories. There's also 1 other way to increase your factory efficiency: production chains. When you hover over a factory you will see the goods it needs to make its products. If those goods are available in the province the factory is built in you will get a throughput bonus of up to 25%. For example if you have a province with both grain and coal you can create a glass factory there followed by a liquor factory. Glass factories require coal whereas liquor factories require glass and grain, so in this scenario your glass factory will get a 25% throughput bonus for having coal in the province and your liquor factory will also get a 25% throughput bonus, 12.5% bonus from having glass in the province and 12.5% from having grain in the province.
So in order to have the most efficient industry you can have you want to focus on the goods your provinces have available and build factories in proper production chains. Keep in mind that your states won't have all the necessary resources in them, many of which you will get from your colonies and spherelings, and the global market for the rest. Some industries like Liquor can be efficiently built in the UK itself, as can Fertalizer, Steel, etc. Others like Textiles won't as the raw materials needed for the Textiles industry are gained primarily from India, where you only have colonies not states(so you can't build factories directly in India). So you should first prioritize the most efficient factory chains in the appropriate provinces, for example the Artillery chain(Fertilizer, Steel, Ammunition, Explosives, Artillery) in Wales and industries like Textiles in places with useless industrial RGOs like the 3 Irish provinces. Even if you don't have the raw materials for Textiles you still want to build the entire chain in a single province to get at least partial throughput bonuses, so make sure to build the Fabrics, Regular Clothes and Luxury Clothes factories in the same province. Same for Lumber, Regular Furniture and Luxury Furniture and other factory chains.
