HSK,
I've gone over the program objectives and the prospectus - it looks like pretty well-rounded. In terms of reputation and recognition, any and all social science discipline that are affiliated with LSE are considered competitive with the top-tier schools around the world... and the reputation is acknowledged in academic as well as practitioner circles. So yes, be it business, economics, policy, law, or public administration... all are well regarded.
I'm not too familiar with LSHTM though, so can't comment on that.
In terms of Health Policy as a discipline in Canada being in its infancy... I'd have to disagree somewhat. Many Universities have been offering health policy related programs for many years... although schools tend to specialize in sub-disciplines. McMaster has had a collaborative program in Health Policy at the graduate level for more than 20 years now... similarly, U of T has had a Health Informatics program for a few years now... and York's School of Health Policy & Management is by far the best in terms of an undergraduate program in Health Policy.
The new initiatives you've mentioned are perhaps "new" in the sense that some of the older programs will now have a new home and the b r a nding of the programs might be different. Also there may be dedicated faculty and specialized resources that won't have to be shared with other faculties. Again, depending on how these programs get implemented, this may be a good or a bad thing. I'd have to check them out before I can say more.