The bat, which was signed by 82 Test and county cricketers, including Jessop and Hobbs, and was presented by Grace to the Friends of St John's Hospital in London in 1907, raised pounds 1,035.
A silver gilt medal given to Grace by the Balloon Society of Great Britain after he scored 1,000 runs in May 1895 raised pounds 1,552.
But it was a rare book by T Boxall, entitled Rules and Instructions for Playing at the Game of Cricket which proved the star of the sale at Phillips in London - fetching pounds 5,520.
A spokeswoman for the auction house said: "This is a very rare book which dates back to 1804. It was last sold in 1966 for pounds 58, so it proved a good buy for the last owner."
Other items at the auction included a bat used by the then England captain Tony Lewis, during his innings of 70 not out against India in Delhi in 1972, when England won the first Test of the series.
A dark blue England tour blazer worn by fast bowler Bob Willis on the India and Sri Lanka tour of 1981-82 also went under the hammer.