The richer sort of people, especially the nobility and gentry from the west part of the city, thronged out of town with their families and servants in an unusual manner

From A Journal of the Plague Year by Daniel Defoe.  

I lived without Aldgate, about midway between Aldgate Church and Whitechappel Bars, on the left hand or north side of the street; and as the distemper had not reached to that side of the city, our neighbourhood continued very easy. But at the other end of the town their consternation was very great: and the richer sort of people, especially the nobility and gentry from the west part of the city, thronged out of town with their families and servants in an unusual manner; and this was more particularly seen in Whitechappel; that is to say, the Broad Street where I lived; indeed, nothing was to be seen but waggons and carts, with goods, women, servants, children, &c.; coaches filled with people of the better sort and horsemen attending them, and all hurrying away; then empty waggons and carts appeared, and spare horses with servants, who, it was apparent, were returning or sent from the countries to fetch more people; besides innumerable numbers of men on horseback, some alone, others with servants, and, generally speaking, all loaded with baggage and fitted out for travelling, as anyone might perceive by their appearance.

This was a very terrible and melancholy thing to see, and as it was a sight which I could not but look on from morning to night (for indeed there was nothing else of moment to be seen), it filled me with very serious thoughts of the misery that was coming upon the city, and the unhappy condition of those that would be left in it.

Parallels with today:

Once the public became convinced it was real, we had exactly the same response - rich people and people who could afford it removed themselves from the city to remote estates or places of refuge.  Poor people and those with too much at stake in the city remained.   

There is nothing intentional about the class divide other than basic human decision making bounded by the practicalities of income generation and wealth accumulation.

With three and a half centuries of relatively free market economies, a far higher portion of the wealthy and productive have been able to effectively ride out the pandemic with only modest disruptions.   It will likely be a few years before we have a good read on just hard the pandemic will have been on the middle class and poorer but the hardships have been real.

In 1665 London and the plague, the stakes were higher.  Remaining in the city was to roll the dice with your life as the stakes.  Many had no choice but to do so.