The English Channel was formed long before that, but there was a low-lying area in what is now the North Sea; but that disappeared, and Britain became an island, about 6000 BC:
Lost world warning from North Sea
Archaeologists are uncovering a huge prehistoric "lost country" hidden below the North Sea.
This lost landscape, where hunter-gatherer communities once lived, was swallowed by rising water levels at the end of the last ice age.
...
As the temperature rose and glaciers retreated and water levels rose, the inhabitants would have been pushed off their hunting grounds and forced towards higher land - including to what is now modern-day Britain.
"In 10,000 BC, hunter-gatherers were living on the land in the middle of the North Sea. By 6,000 BC, Britain was an island. The area we have mapped was wiped out in the space of 4,000 years," explains Professor Gaffney.
So far, the team has examined a 23,000-sq-km area of the sea bed - mapping out coastlines, rivers, hills, sandbanks and salt marshes as they would have appeared about 12,000 years ago.
http://news.bbc.co.uk/1/hi/education/6584011.stmBut small boats have been found in the area from that period:
# Pesse logboat, Netherlands. Found on land, dated to ca 6300-7000 BC. 3 m long and made of pine tree. Described in an article by Detlev Ellmers in The Earliest Ships (Conway Maritime Press 1996).
# Logboats of French inland. Three different finds have been made in the Seine valley area near Paris. The finds were made between 1984 and 1994. They are C14 dated to between 6400 and 7200 BC. Replicas have been made by GRAS. Ref Philippe Bonnin: Découverte de deux pirogues monoxyles mésolithiques entre Corbeil-Essonnes (Essonne) et Melun (Seine-et-Marne). Report.
# Hardinxveld-Giessendam logboat, Netherlands. Excavated on land in 1998, 5.5 m long, dated to c 5000 BC.
http://www.abc.se/~m10354/uwa/wreckeur.htm