In the 16th century, King Henry VIII enacted a religious reformation in England, taking it from Catholic to Protestant. At the time, the Catholic church, headquartered in Rome, owned a HUGE amount of real estate and consequently revenue in England--something like 1/4 of all land revenue went to to the church through tithes. A large component of that went to religious houses--abbeys, convents, monasteries, etc--and the lands attached to them. As Henry VIII acted to make England the center of its own church, the Anglican Church, he seized the assets of the Roman Catholic Church and appropriated them for himself. This took place over much of the 16th century, but is particularly notable during 1536-1541, when he enacted laws referred to as the Dissolution of the Monasteries, when he, well, dissolved the monasteries and took possession of all assets. Sadly, many documents and buildings ended up being destroyed, and the UK is dotted with picturesque ruins as a result, and untold numbers of early documents are gone forever. The King used these former church assets at his discretion, meaning that he kept some of them for himself, and he gave others to his supporters and sold others off. So the fictional Downton Abbey would have perhaps been given to someone, maybe someone the king elevated to the nobility. Or it might have been sold off, with some wealthy person purchasing the building from royal properties. Over the years it could have been sold again. Or seized and given again. Whatever the case, the term "Abbey", because of this colorful history, gives the building an air of ancient mystery and grandiosity. When the protagonist of Northanger Abbey visits the titular home for the first time, she wonders if she's going to find some romantic, stormy ruin, and is disappointed to discover that it's a very nice building that has many modern conveniences and harbors no dread secrets.

Check out The Stripping of the Altars by Eamon Duffy for more information on what went on and how these buildings ended up in private hands.