Before The Beginning of Time
Genderless (personified as Male)
God is a primordial being who is generally believed to be the omnipotent creator of all and to have simply existed before, and outside of time and space (having created such things). Little is known about him, but the fact that Christian exorcism rituals can force Ghosts to cross over would suggest the God in the BBC Being Human universe to probably resemble the Abrahamic depiction common to Judaism, Christianity, and Islam. He is described as male, but is ageless and without true definition of gender and otherwise.
Jesus Christ is said in Christian lore to be the Son of God, sent to Earth 2,000 years ago as his vessel and the Messiah. Captain Hatch once implied that the miracle of turning water into wine - which Jesus is known for being said to do in the Bible - was in fact truly accomplished would suggest that Jesus was indeed God's son or in the BBC Being Human universe at least possessed some power or abilities. (The Last Broadcast)
According to Captain Hatch, God created the Devil to cause chaos, death and corruption as part of the natural order. Hatch also claimed that God made humans to be a species capable of surviving and existing independently of God, so that he could "retire" from creation and return to what Hatch described as "gardening and wordsearch puzzles". (The Last Broadcast)
When John Mitchell and Lucy Jaggat argued over their differing views on God and what supernaturals were like to him, Mitchell pointed out a hole in Jaggat's anti-supernatural beliefs by questioning why God allowed supernaturals to exist in the first place. Mitchell also believed that as Humans were made in God's image according to lore, this would include God's rage, spite and indifference.
The brutal treatment of the dead by the Men with Sticks and Rope on the Other Side would suggest that in the BBC Being Human universe, God is concerned more with upholding strict celestial law than with empathy or benevolence towards humans. (All God's Children)
Powers and Abilities
If various scriptures and religious lore are to be believed, God is all-powerful, or omnipotent. He is the ultimate authority, ageless and eternal; he was never created or born, he has always existed and always will exist. He is also all-knowing and all-wise, or omniscient. He knows everything that can be known or learned, and he never forgets.
Captain Hatch's words to Dominic Rook certainly implied that God was the creator of all reality, the guiding hand behind evolution and the designer of all beings, including Hatch himself.