If you look at the beachead (9-13 June) development map; notice V Corps advanced from Omaha beach. They may have been stuck on their beach the longest but they really didn't waste any time once they were ashore!
Here's another from Operation Overlord. This one is a little more clear of the overall picture, especially the Airborne landings. By the way, the top one of the whole thread...it's off Call of Duty!
What did 1 Can Para do on D-Day? I know what 6th Airborne did but the only precise knowledge of a regiment was the 2nd Ox and Bucks taking Caen De Canal bridge.
All I know is that they were there as a part of the 3rd Brigade of the British 6th Airborne Division. I haven't looked much into it. I really should I suppose.
They also participated in the Battle of the Bulge and the Rhine crossings of Operation Varsity.