My ds's both had a great time at school after SATs. It was when they had their week long residential trip, there was another day trip related to their topic, and as the vast majority went on to the local secondary, there were visits from the teachers there and they visited the new school a couple of times as well.
Then a lot of time was taken up practicing for the leavers concert, and a leavers service at the church because it was a CofE school.
They had sex education lessons after SATs as well, all fairly basic and mild stuff stuff though.
Other lessons focused more on their topic than on SATs work, but they did still have proper lessons as well. My ds's particularly enjoyed maths lessons after SATs, as rather than just learning maths formally, they did mathematical investigation type projects. I can remember it that well, but one of them was where they had to work in groups and make business plans and calculate expenditure and profit and that sort of thing.
In my experience, they got a lot more learning out of school in the months after the SATs than they did in the months before.