The Taiwan mulberry probably won't do well here in the UK - it prefers temperatures to be around 23-25 deg C year round, or at least, the newer hybrid Morus atropurpurea (syn M. alba) Miaoli No. 1, bred in 2008, does. It also does not appear to be self fertile.
Morus macroura, the Pakistan mulberry, is available in the UK - it will need full sun and free draining soil, and although it should be hardy in Zone 8 (most of the UK) it will not appreciate cold, wet winters much. Known as a 'low chill' tree, it would prefer temperatures no lower than -5 deg, but will tolerate down to -15C. However, as with many plants in the UK, its the combination of cold and damp that might be an issue and that might affect fruit production. It's said to be self fertile, and is listed with Reads Nursery, 01986 895555. Link here