That ship is going to have to be deballasted one way or another as tugs are most likely not going to be able to unground it.
So the process largely depends on her pumping systems and the amount of deballasting she can accomplish under that load. Chances are that there's not much, would be my guess.
As remote as it appears to be, not much likelihood of cranes being able to reach the containers (although some could be). Now you're talking heavy-lift helicopters or - if there's a heavy-lift vessel nearby (such as up in Cyprus where there's some big offshore installations), they could bring that in.
In any case, you're looking at maybe a week's worth of work before it can be straightened back into the channel if the tugs can't float it free. And you almost have to assume there's been propeller damage done, so she won't likely be under full power. Lloyd's of London no doubt already have people in place to assess their losses. Could be a big drydock bill coming up, might be that they just write off the asset.
And after that, there'll no doubt have to be a seismic survey run to check for channel damage that this beastie could've easily done.
