There were quite a few different reactions, and panic was probably the main one. People didn't understand much about disease in those days so some of what they did wouldn't make much sense to us today.
Here's one reaction before the plague came to England - yes, people knew it was coming:
By June 1348, the plague was in Paris, but the fear of it travelled
more swiftly and England watched and prayed.
from historyanswers
King Edward III didn't show any signs of panic - he carried on as normal and even held tournaments instead of resorting to "excessive religious fervour and abstemious living in the hope that God would see fit to keep them safe". Later he was more cautious and left plague-infected London.
For the population in general, sciencemuseum says
With no accurate knowledge about the disease and the way it was
spread, what could be done in the face of such horror? While many
followed Hippocratic advice and fled, others waited.
Here are some other things people did.
The people of the Medieval Ages were uneducated about diseases and
cleanliness. Many thought it was caught through the air, so they would
burn incense like juniper and rosemary to try to prevent infected air.
People would dunk their handkerchiefs in aromatic oils to cover their
nose and mouth from the air. Another common remedy was the cure of
sound. Church bells would ring to ward off the plague. Church bells
were often rang during a crisis, so they felt this was a justifiable
remedy. Sometimes cannons were fired because they were so loud. Local
apothecaries made a lot of money off people during the plague years by
selling and marketing all sorts of talismans, charms, and spells for
protection.
from https://sites.google.com/site/theblackdeathmary/medical-prevention
Also, there were some religious fanatics called The Flagellants. These were more common in Europe than in England but 600 came to London and beat themselves in "Attempt to Repel the Black Death".
from http://www.eyewitnesstohistory.com/flagellants.htm
The question specifies England but one interesting reaction in neighbouring Scotland involved taking advantage of the plague by invading England. A BBC article quotes Henry Knighton who wrote
The Scots, hearing of the cruel plague of the English, declared that
it had befallen them through the revenging hand of God, and they took
to swearing by 'the foul death of England' - or so the common report
resounded in the ears of the English. And thus the Scots, believing
that the English were overwhelmed by the terrible vengeance of God,
gathered in the forest of Selkirk with the intention of invading the
whole realm of England.
http://www.bbc.co.uk/history/british/middle_ages/black_01.shtml
