I'll try to answer it, but i have to talk about some of the premises in the question as well. It's a pretty wide question that essentially asks about "all" legal cultures and a millennium of legal history in England and the continent. I'll first give some general thoughts on the question and then talk about the origin of common law and why it is different.

I won't be able to cover the full developments of the modern systems, and will just provide some comments on why and how England developed it's own system. I think asking "what made england different" is better (easier to answer) than asking "why didn't everyone else do as England". If the comment is a bit messy it's because there are many different things that need to be mentioned.

General comments on the question and on the common/civil law distinction

Common law didn't arise anywhere else because common law refers to a subset of English law, it - by definition - is English. Common law is often used to refer to a (family of) legal system(s), but it takes it's name from rules called the common law, as a set of case-law in the english legal system. The only reason other places use it is because they use(d) english law and built on it. Old english common law is still legally relevant, where not changed, in other common law systems.

Non-common legal systems and cultures also have court decisions and precedents, rulings from the German Constitutional Court has the status of law, and rulings from the European Court of Human Rights are typically important as well. Other European courts also have important precedents even if their rulings don't operate within the common law logic of "stare decisis" (let the decision stand). I'm just saying this to illustrate that neither case law or precedents are unique to common law, even if their practical importance can be larger.

Using strong court precedents isn't the only way to make rulings "consistent", in fact - consistent rulings has arguably been a larger focus in continental law than in common law, by way of developing general principles of law that could give a coherent and logical result in every case. Civil Law countries have sometimes been more sceptical of dissents for this reason, that it makes the law seem illogical and inconsistent: judges pronounce the correct law, they don't make it. But again here there is a large difference between francophone and germanic civil law, as german judges argue their point while french pronounce it.

Common law vs. Civil Law isn't always the best generalisation of differences between legal cultures either, for example the US and the UK belong to very different constitutional traditions. Norway and American are different in civil/common law, but both use the "american" court structure of generalised courts, compared to the use of more specialised courts (The "austrian" or "european" model). On the other hand, Norway has "civil" inquisitorial judges while the US and common law countries typically have adversarial judges.

Some civil law countries use a generalist legal education (there is one "law" study for all legal jobs) like what is common in the UK and US, which we can call a generalist legal system. Some countries specialise a lot with different studies or different paths for different legal jobs, which we can call a specialised legal system.

Even the usage of "legal codes" don't really follow the civil/common divide. The Nordics don't use codes for the most part, rather regulating by individual statutes. But in terms of legal methodology, theory, ideology and often content of statutes - they tend to follow the continental systems, and are typically categorised as "civil law".

The point is that the distinction isn't that useful in practice, in my opinion. It gives a lawyer very little to know whether a system is "civil" or "common". There are attempts to generalise the differences, but any such generalisation tends to not be correct for every civil- or common law country, illustrating that these aren't actually systems. Rather, the terms are a very generalised picture of mostly a legal cultures history. Especially "civil law" today is many different legal cultures that often share some of a larger set of traits. "Common law" countries are a bit more coherent as they are fewer and developed from the same legal culture, but there is large variation as well. In total, common and civil law should not be thought of as actual and defined systems.

Continued below