Wilfred Mott was the father of Sylvia Noble and the maternal grandfather of Donna Noble. He was also a one-time traveling companion of the Tenth Doctor. A witness to several alien invasions of Earth in 2009, he was instrumental in stopping the Time Lords' return from within the time-lock which had sealed them in the Last Great Time War. In that effort, he trapped himself in a chamber about to be flooded with lethal radiation. His rescue was the proximate cause of the Doctor's regeneration into his eleventh incarnation.
Wilfred had a positive attitude. Even in a crisis, he turned to good war-time spirit. He was a strong patriot, loyal to Queen Elizabeth and his beloved England. He also had a good relationship with his granddaughter Donna Noble and encouraged her companionship with the Doctor, even keeping it a secret from his daughter, Sylvia, for a time.
After the Doctor had to erase Donna's memory in the aftermath of foiling Davros's latest plan, Wilfred's strong spirit seemed to have gone. That was probably because he believed that she was better with the Doctor. As the TARDIS dematerialised, Wilfred saluted in respect.
Wilfred also proved a loyal companion to the Doctor, from searching him out when prompted to by the mysterious woman, to giving the Doctor his gun and prompting him to kill the Master, as well as serving as a gunner when the ship they were on was under attack. He convinced the Vinvocci to bring him back to help the Doctor. He also showed a willingness for self-sacrifice by saving someone trapped in a radiation booth and being willing to die there so the Doctor could live, saying he was an old man.
He developed a paternal relationship with the Doctor, trying to comfort him when he began to cry during their conversation and wanted him to be happy and have someone to make him laugh. He was also willing to give up his life to let the Doctor live. This relationship was picked up by others, with the Master sarcastically referring to Wilfred as the Doctor's father. Wilfred admitted he would be proud to have the Doctor for a son and the Doctor said he'd be honoured if Wilfred was his father.
At Donna's second wedding, Wilf met the Doctor one last time. The Doctor gave Wilf and Sylvia a winning lottery ticket he had purchased with money borrowed from Geoff Noble, then left. Wilf and Sylvia gave Donna the ticket and Wilf tearfully saluted the Doctor as he took off.