Gemma Arterton was the first name i thought of as she is known to the US audience through Hansel & Gretel, One of the Bond films, Prince of Persia amongst others.
Just curious.... why is everyone assuming that that Lara Croft in the reboot is even going to be English?
As has been seen with other reboots, they are happy to change things to fit with what they want to do. The Raimi version of Spiderman's origin wasn't the same as the comic. The reboot wasn't the same as either of those two.
If they wish to reboot it and have Lara Croft as some American "socialite" they will do it, especially if they can get the actress they want for the role.