This is likely Zoids. Animal-shaped mecha and TV Tropes notes that:
The animated series takes a lot of inspiration from the Gundam franchise, with the first two series having a war theme and later series lightening it up with a tournament storyline.
And indeed, it was shown on Sky TV around 2005, possibly as a rerun as people were talking about it being shown "again".
Wikipedia summary of Zoids: Chaotic Century:
Zoids: Chaotic Century is the first Zoids anime series. Its setting is loosely based on that of Battle Story, and follows Van Flyheight as he meets an amnesiac girl called Fiona and a small Zoid called Zeke. As the series progresses, Van meets various opponents, such as Raven, and friends, like Moonbay and Irvine, and eventually ends up helping Fiona in her quest to regain her memory and to find a mysterious entity called the "Zoid Eve". Their quest takes them into the thick of an ongoing war between the two factions of the Helic and Guylos.
And of Zoids: New Century Zero:
Zoids: New Century Zero takes place some time after the events of Guardian Force, however, aside from a few cameo appearances, there is no direct relation to the past series. In New Century Zoid battles have become a tournament-based fighting competition. The main character is Bit Cloud, a junk dealer, who forms part of the Blitz Team. He becomes a pilot of their Zoid, the Liger Zero, a temperamental Zoid that previously had been unpilotable. Bit and Liger form a partnership and end up joining the Blitz Team in their various league matches. He is aided by his teammates, Leena Toros, Brad Hunter, Jamie Hemeros, as well as their leader, Dr. Steve Toros.