Hello,
I have a doctorate in Tissue Engineering from the UK. The first centre for TE in this country was University College London (UCL) where I studied for my PhD, but several other Universities conduct research including Birmingham, Manchester, Sheffield, Liverpool. With regards to stem cells, UCL has some interesting work from several separate groups including Dr. Stephen Minger and Dr. Chris Mason (Tissue Engineering). I would go to one of the regular Regenerative Medicine conferences to make contacts about prospective PhD projects in this area.
Good luck.