At the Battle of Britain and throughout World War Two, did the Allies have aircraft carriers in The English Channel to further extend the

I can find no references of them being deployed in the channel. Strategically it would have made no sense. The Battle of Britain was a defensive one for the allies and aircraft were not being deployed across the channel for offensive purposes. A carrier would have been a sitting duck for axis submarines.
Are you taking a Naval history class? This post was edited by Element 99 at July 24, 2019 7:18 PM MDT

No.
The fighters had enough range to reach the continent, as it was.
And they could add external fuel tanks to extend that range, as they did to escort bomber flights.


EDIT: The width of the English Channel is about 150 miles.
The range of the Hawker Hurricane fighter was 600 miles.  (inflicted 60 percent of the losses sustained by the Luftwaffe in the Battle of Britain)
The "combat radius" of the Spitfire Mk VB was 410 miles. This post was edited by Walt O'Reagun at July 24, 2019 10:16 AM MDT

No they did not.  Mallory and Dowing used Radar to concentrate their forces to counter the German thrusts.  Spits and Hurricanes had enough range to reach France with limited time over target.  Same for the Germans with the ME109's and FW190's.  Do note the Germans fighters only had approximately 10 minutes over target escorting the Bombers.  The ME110 was put into action as a fighter which it was not, a fighter Bomber role would have been more suited.

What beat the Germans was tactics.  The Brits took off only in the Nick of time allowing them to stay up longer.  Hurricanes were assigned Bombers, Spits Fighters when possible. 

We have a relative who is almost 100 who flew ME 109's then transitioned to FW190's.  He finished the war flying ME262's

My Dad flew P47's then P51''s these had the range w/o drop tanks to play H___L in Northern France.  The P38's had the range to go to Berlin and back.  Per my Dad and others the P51 was a cheap bird, the P47 and P38 were double or triple the price of a P51.  The P51 also had a performance breakthrough when they put in Merlins instead of the lousy Allison which hobbled the P38