Ianto Jones' father

Mr Jones was the husband of Glenda Jones and father of Ianto Jones and Rhiannon Davies.

Biography
Mr Jones worked at Debenhams, but his son — with whom he did not have a good relationship — told people that he was a master tailor capable of correctly determining a man's inside leg measurement by his stride alone. (TV: Something Borrowed, Children of Earth: Day Five)

Ianto claimed that his father enjoyed taking him to the cinema, (TV: From Out of the Rain) but Rhiannon implied that their relationship was not as strong as he made it out to be. He once pushed Ianto too hard on the swings in his childhood and caused him to fall, breaking his leg. (TV: Children of Earth: Day Two)

Ianto moved away to London due to his father disagreeing with his life choices; (AUDIO: New Girl) he repeatedly told Ianto that working in the steelworks or fixing cars was a proper job. (PROSE: Trace Memory) However, his father found him and forcibly moved in with him. He tended to break in if he could not find the key, pass out drunk and wake up periodically to urinate on the carpet. Yvonne Hartman offered to retcon Ianto's family, purging their memories of Ianto's father, but Ianto eventually decided against it, saying his sister deserved to have a father. (AUDIO: Blind Summit)

In the last days of his life, he was hospitalised and waited three weeks for a call from his son, in vain, before he died. Ianto, dreading emotional upheaval at the thought this would without a doubt be the final time he spoke to his father, could not bring himself to say goodbye. (AUDIO: The House of the Dead)

Along with other dead people, he was "summoned" by the entity Syriath in the House of the Dead. He talked with a "revived" Ianto Jones, holding his "betrayal" against him. He tried to persuade him to let Syriath rise, in order to see again his passed loved ones such as his mother, Owen, Toshiko and Lisa. He disappeared along with every person "resurrected" by Syriath when Ianto sealed the Cardiff Space-Time Rift forever. It is unclear if this was the real Mr. Jones or an illusion crafted by Syriath. (AUDIO: The House of the Dead)

Behind the scenes
He was credited as "Mr Jones" in The House of the Dead. The full name of Ianto's father, however, has not been revealed.