A lot of the older breeds of draught horses were really larger than needed for a small homestead. Mind you, they are great for day in and day out ploughing on a larger basis for a big working farm; the Amish still use them extensively. But you can get by with smaller multi-purpose breeds on smaller acreage (under 300 acres)
My Uncle logged for decades with a team of mix breed horses of only about 1200-1300 pounds each. And even after switching to tractors for the logging, he and others continued to farm with horses of 1000 pounds or slightly less, single hitched.
In fact the relatively diminutive Morgan breed was developed as just such a multi-purpose breed. When I was a kid (from about age 8 through 15) I had a Morgan that was my saddle horse and Daddy's plough horse. We farmed (kitchen crops) about 10 acres with him and I competed in saddle events at shows with him.
We also have a long tradition of using smaller mixed-blood horses of many types to work the land, take the produce to market and the family to church/chapel as well as being decent quality saddle horses, but there are some distinct differences between here and your side of the pond.
The first and most important of these was WW1, when huge numbers of the best of the bloodstock, the harness and a good deal of the various implements were requisitioned for the war effort and sent to Flanders, along with most of the men who held all those generations of horsemastership in all it's guises; none of the
materiel came back from there and very few of the men and horses. At the end of the war the remaining bloodstock was of a very inferior standard and harness makers along with the agricultural engineers who built the small-scale farm machinery had been decimated, and all the people could think of was the promise of affordable tractors and technology; only those who absolutely had to use horsepower had to make do with what they could get their hands on and all the old standards went by the board.
As tractors and suchlike did indeed become affordable for some, those people found they were now in a position to buy up land from the smaller
homesteaders, and horses became used less and less, apart from the bigger farmers who held to tradition and used large teams of big draught animals to work large parcels of land. And so it went for some years, and the old implements were left about the land and fell into disuse.
Then along comes WW2 and the imperative for scrap metal to go towards, again, the war effort; the first things to go were all the old iron things
lying disused in the yards and fields. What didn't get taken this way ended up years later on the forecourts and the walls of pubs, hotels and the like.
As a consequence of all this, for many years the only old horse-drawn implements to be had were the big ones suitable for the larger draught breeds as even the bigger of the landowners found it impossible to ignore the new mechanisation and let the horse teams go.
It's true that there are a huge number of horses in the UK, but you don't need to look for long at the situation to realise that an awful lot of them aree kept as little more than pets on small patches of terribly horse-sick paddock, and a lot more than you'd imagine see nobody for days on end and are left in misery
and poor health by people who have no idea of what they need, and even worse don't really care. The situation in this green and pleasant land is, I'm afraid to say, dire.
I know whereof I speak, having spent many years now involved in horse rescue and rehabilitation.