The law of every country in the English-speaking world started that way. Australia's current system of law, for example, commenced as a branch of British law on 26 January 1788. All the laws in force in Britain at that moment were presumed to apply; laws governing institutions and issues peculiar to Britain-as-a-place just weren't of any consequence.
Periodically you go into the collection and clear it out. In Australia in the 80s and 90s there was a law reform movement and as a positive side-effect enormous research was done to discover the true coverage of "Imperial" laws still technically in force. Our various Parliaments passed various Acts to repeal and replace old laws.
For example, where I come from, in the Northern Territory, the Law of Property Act repealed laws going all the way back to shortly after the Norman conquest.
Yep. Or you give yourself a new constitution and say "All laws previously in force automatically come into force, unless they contradict the new constitution". Ireland did that.
Likewise Ireland cleared out a lot of old laws in the 200X's. It was done by saying "Anything pre-1922 is repealed unless it's on this list".
I'm unsure why they kept some laws, like the 1204 law on "Erection of castle and fortifications at Dublin; establishment of fairs at Donnybrook,Waterford and Limerick", but at least now we can refer to it as the Fairs Act of 1204....