Whilst the image is one of London being gripped by terror it was still very much carry on as you were. Whitechapel in particular was a notorious working class area at the time and murders would happen frequently. It also didn’t help that the press were reporting on the Ripper murders with a large surge of faked communication from the murderer or murderers being sent in. It’s no different to what we see today with the media going to town on a good story, and serial murder is a good story. One for comparison would be the Ipswich killings a few years ago. People had little choice to carry on with their daily lives. The generally accepted run of Jack’s murders were from August to November, but there were cases before and after that whilst not identical, certainly had very similar modes of execution.

Two good books I can recommend to give you an idea of that area of London around the time are The People of the Abyss by Jack London, and They All Love Jack by Bruce Robinson. Whilst the latter book is more of a serious attempt to remove the mythology that’s built up around the Ripper, it does give you an extensive idea of what the area of Whitechapel was like at the time. Both are worth reading but quite a big commitment.

The TLDR: People carried on with their lives as per usual, the media made a meal out of them.