What's the meaning of the label MRE and a number like 162 or 600 in the names of bacteria?
MRE is an acronym for the Microbiological Research Establishment at
  Porton Down, UK.


It was applied to Escherichia coli strain MRE600 as that was where the strain was first deposited, according to this paper.

I tracked the answer down in an article by Chris Morris on the Culture Collection Page of Public Health:

“My association with Porton Down, the current location of the European Collection of Animal Cell Cultures (ECACC), started at an earlier date than the inception of ECACC, and was when the site was known as the Microbiological Research Establishment (MRE), part of the Ministry of Defence.”

The numeric portion of the strain designation (600 etc.) that follows MRE is presumably just a reference or accession number within the institute, with no biological meaning.

(As a matter of interest, Porton Down had a certain notoriety in Britain back in the ’60s as a secret military establishment.)