Economic history entry reqsWatch
That said you are still in with a shot if you can put together a good personal statement that shows a real interest in economic history. I know that advice is probably not all that helpful on its own but they will be able to tell if you have a passion for the subject, it will show through. Have a look at the personal statement guidelines they give on the LSE econ history prospective applicants page. You've also just about got time if you wanted to maybe try and pick up a few (related[!]) books off the indicative reading lists for some of the EH courses on the calender to write about if it came to it, though that may not come across entirely convincingly (of course if you've already got a particular area you're interested in which you've read around and could write convincingly about, that would be ideal).
My own grades were not really stellar by LSE standards but I think the fact that I managed to pull together a good personal statement may have made up for it. Good luck!