No, London (and Greenwich!) are not on GMT. Right now they are one hour ahead of GMT (British Summer Time).
If you have a "dumb" clock, you can just set it to UTC as per WWV and be done with it. If your clock is "smart" and corrects for daylight savings time, you may have more difficulty.
The Windoze Control Panel Date/Time dialog box has a setting called "Greenwich Mean Time: Dublin, Edinburgh, Lisbon, London". IIRC, this is not actually GMT, it's British Time. At a large Field Day station a year or so ago, we had one or two station managers that had set their computers to "Greenwich Mean Time" but who had not unchecked the "Adjust for Daylight Savings Time" check box, and whose logs were wrong by one hour as a result. I seem to recall being told that the "Casablanca, Monrovia" setting is actually GMT all year round, but I haven't taken the time to verify this.