Well to be perfectly up front, I'm not a "real" Baptist. I attend a Southern Baptist Church but we are not members nor do we plan to become members.
I'm not sure of the context of Spurgeon's remarks. My GUESS is that he is eluding to the fundamental principles of Christianity (e.g. evangelism, charity, helping the poor, etc). These principles are part of the universal church and TRUE believers have always believed them. Consequently I BELIEVE he was referring to the true invisible church apart from the Roman Catholic and the Reformation Protestants. I could be wrong.
Baptists are notorious for focusing on evangelism to the exclusion of doctrine. Consequently most Baptist churches have very loose Statement of Faiths. They're also, for the most part, self-substaining with little hierarchy.
In the History of the Reformation series it briefly talked about the Anabaptists and I wondered if this was the beginnings of the Baptist belief. If you read the London Baptist Confession of Faith of 1610 you'll see there is little difference between their Reformed beliefs and the Westminster Confession of Faith. However, unlike the Presbyterians and Lutherans, Baptists believe in Credobaptism (immersion) verses Paedobaptism (covenantal infant baptism). There are other differences too much to go into here but they hold to some of the more fundamental principles.
Like many of the Protestant churches today, Baptists are losing their original Reformed doctrine. You will find many of them arguing the Roman Catholic position of Erasmus of man's free will. This wasn't how it originally was but it is how it is today.
Religion comes in two flavors; Augustine or Pelagius, Luther or Erasmus, Reformed (monergism) and all else (synergism). There are only TWO religions in this world. (Click on my name for further explanation.) That's how it is.
"What were the Baptists reforming then?"
Knowing Baptists, they were probably reforming other Baptists, just as they are today. To paraphrase scripture "where two or three Baptists are gathered there are at least five or six interpretations".