You would need to check your specific carrier of choice in these countries. I pulled this from the wiki, so it probably isn't complete. But afaik, only the iphones and the nexus 6 has any decent amount of lte bands in the areas you are asking. particularly, the unlocked iphone bought directly from Apple (NOT the verizon one)would be the most compatible. it would cost the same as the verizon version.
Taiwan - 28,8,3
Singapore-3,7
Hong Kong - 3,7,8,40
France - 3,7,20
UK-3,7,20,42,43
Germany-3,7,20
Japan-1,8,9,11,18,28,41
ip6/6p
Model A1549 (CDMA)*
Model A1522 (CDMA)*
LTE (Bands 1, 2, 3, 4, 5, 7, 8, 13, 17, 18, 19, 20, 25, 26, 28, 29)
Note that the unlocked iphone which Apple sells does include bands 40 and 41. This will work on Verizon, however, the Verizon version does not have these two bands.
Nexus 6
LTE (2, 3, 4, 5, 7, 12, 13, 17, 25, 26, 29, 41)