Why battle-line speed mattered for crossing the T

If Britain wanted battlecruisers, why also increase the speed of its battleships?

A faster battle line gives greater control over engagement geometry and improves the chance of crossing the enemy's T.

Britain wanted battlecruisers for mobile global missions but also wanted its battleships to become faster. In a line-of-battle artillery engagement, superior speed helps an admiral choose the approach and maneuver across the enemy's course. Crossing the T lets more friendly guns bear while restricting the opponent's return fire. The modernization goal was therefore tactical control for the whole battle line, not merely keeping up with fast scouting forces.