It is in Chapter 45 that we find the final answer to all of the suspicion and curiosity concerning the exact nature of the "friendship" between Annie Strong and Jack Maldon, when Annie has a sentimental and honest heart-to-heart with her husband, Dr. Strong, and is honest about what has been happening between her and Jack. She reveals that they were at one stage lovers, but fortunately fate intervened and she married Dr. Strong, which she is very relieved about:

"We had been little lovers once. If circumstances had not happened otherwise, I might have come to persuade myself that I really loved him, and might have married him, and been most wretched. There can be no disparity in marriage like unsuitability of mind and purpose."

She declares that she has not spoken one word to Jack Maldon for a considerable time, and also reaffirms her true love for her husband, Dr. Strong, and explains how she has realised the true character of Jack Maldon and wished to have no more to do with him, in spite of the suspicions and rumours of others. So, in answer to your question, it is clear that Annie Strong never had an affair with Jack Maldon.