Look at where past graduates have gone on to, from your alma mater. If there's no one who broke into top 10, realistically, you can't expect any different, unless you were an anomaly during your undergrad (top of cohort, or something like that). Next, did you get a distinction in your masters at LSE? If so, look at whether past graduates from that programme ever got into economics PhD programmes. It's highly unlikely that the masters will be viewed favourably (more so since it wasn't awarded by the Economics department), but at least a Distinction is better than nothing. Note that schools explicitly mention on their websites that they only view pure economics masters favourably, and heavily discount even applied economics masters, unless you provide them with a complete syllabus vouching for its rigor.
One thing you must always remember during the admissions process. Almost everybody who's seriously applying already have good math & econ grades and decent letters. Having those doesn't make you special. You need fantastic letters from renowned faculty to make an impression. This usually comes from a good RA stint somewhere, prior to admissions.
Also, it helps if you adopt the format for posting your profile here, since many will definitely be deterred by the wall of text in your first post.