The point is that GMT isn't changing, the region is switching to an entirely different time zone, BST (British Summer Time). If your time is based on GMT, it won't change due to British daylight saving time because GMT never changes.
For a similar example, in the part of the US that uses Mountain Time, states observe MST (Mountain Standard Time) in the winter, and most switch to MDT (Mountain Daylight Time) in the summer. However, Arizona doesn't observe daylight saving time, so they remain on MST. MST always stays the same (GMT-7), the time is only changing because the states are observing a different time zone. The same happens with GMT and BST, it's just harder to see because you can't pick out areas that remain on GMT all year.