In England the owner doesn't have the deeds, although they may obtain a copy. It's digital with the Land Registry.
Scotland, incidentally, has the oldest land registry in the world (1617 CE), the Sasines.
I paid off my flat in Edinburgh back in 2016 or so, and in exchange I received a huge bundle of papers "the deeds", from the bank.
I spent a fun evening flicking through the records of owners, the price they'd paid for it, and the few details provided (occupation, etc). All dating back to when the building was built in 1890 or so.
Later I left the country, and moved to Finland. After a year or two here I wanted to sell the flat as I'd decided I wasn't going back. Despite going through the process of ensuring the registry was updated I had to mail them back to the solicators based in Scotland prior to selling the flat.
The sale was carried out 100% remotely; I had a couple of phone calls, and when I balked at the use of a FAX machine I printed out a few forms/documents from emails, signed them, and physically posted them back to the solicators.
Happily I'd had the foresight to leave a spare set of keys with a trusted friend, which were used for the viewings, etc. It probably helped that the solicator who handled the sale had also handled the registration of the deeds when I received them so they were probably confident it was a flat I owned..
When I queried things I was told "The only registry is definitive, but .. things are .. smoother .. with the physical deeds". Made no sense to me, but I wasn't going to argue.
When the land registry was digitised they got the land boundaries from the Ordnance Survey maps. The Ordnance Survey got them from tracing aerial photos. When property changes hands for the first time since the digital system was introduced the land boundaries from the OS mapping agency have to be checked against the original deeds as they are almost always slightly wrong, e.g my kitchen was shown as being partly in my neighbour’s garden according to the digital map.
