Hamsters are native to Syria. The plague is believed to have originated in China in the early to mid 1300s. Hamsters weren't being domesticated until the late 1700s when they were noticed by naturalists of the era.

The first hamsters brought to England were smuggled in in 1930. All modern day pet hamsters descend from those hamsters.

I'm not sure what you read but hamsters could not have been a carrier of the plague in London in the 1600s.