For the sake of accuracy:
Europe did not have the same laws throughout. It wasn't even seen as one place. There was very frequent war between different European countries.
Britain wasn't one country either for almost all of the period of time you mention, so it too didn't have one set of laws.
I'll restrict my reply to England, since I don't know the history of law in other places. Property rights unsurprisingly varied over the ~12,000 year period you refer to and for almost all of that period of time England didn't exist either. Different tribes might well have had different laws, but it's impossible to know since they left no records of their laws. The earliest records are Roman and imply that British women had significant property rights. Roman law at that time gave women significant property rights.
Christianity, unsurprisingly, reduced women's rights in all sorts of ways including but not limited to property ownership, but we're rather short on evidence of law for the early medieval period. It wasn't a Dark Age as such, but it is "dark" in the sense of a scarcity of surviving writing.
The laws you're (somewhat inaccurately) referring to were Norman. Under Norman law, a marriage was a legal entity (rather like a modern company) andlegally the marriage itself controlled the property. Obviously, this didn't apply to unmarried people. Unmarried people, regardless of their sex, could own and control property and other assets in their own name. If you examine medieval records from after the Norman conquest, you will find many examples of women owning property (and land and businesses and everything else). Also, in law a husband couldn't dispose of property without the permission of his wife, since a married person couldn't control property or other assets.
There was very often a lot of anti-female sexism the way the law regarding marriages owning property was implemented, so the husband was often given priority in law even though the law as written didn't explicitly do so in the context of control of property (inheritance of property was a different matter - that was explicitly sexist). But, of course, that only applied to married people. The laws regarding marriage, however they were implemented, couldn't apply to people who were not married.
Also, prior legal agreements could over-ride the default (and often did). People who had money could (and often did) add clauses into a marriage contract to ensure their daughter(s) had an independent income.
The Married Women's Property Acts (there were 2, not 1, and they were passed in 1870 and 1882, not the 1860s) you refer to gave married women superior property rights to those married men had. The marriage controlled the husband's property and assets, but the wife controlled her own. This is the origin of the phrase "What's mine is mine and what's his is ours". That was what the law stated at that time.
Those are not really seperate things, particularly with a religion that so thoroughly permeates into a culture.
