That is wrong. Because GMT was the world standard by which all other timezones were directly measured against (making them either plus or minus set amounts of time in relation to GMT) it is therefore a fixed time point, and can not be adjusted at all without throwing the whole system into chaos. So 1PM GMT is always 1pm GMT.
In other words, even if the local time in Greenwich was itself changed (as it does with Daylight Savings being introduced), that does not change GMT itself, it instead merely makes the area that was GMT now become GMT+1 for a certain length of time (until daylight savings ends, in this case), before it reverts back to matching the standard as was originally set there.
If GMT itself could be changed, there would be no need for the implementation of British Standard Time at all. But because it is a fixed constant, the zero point that every other time zone measures against, GMT itself can never be changed for local conditions, because if the zero point of GMT suddenly changed, then every other time zone would also have to make adjustments worldwide in order to maintain the correct correlating times. Effectively meaning that if the UK adjusted their clocks then everyone else in the world would also have to do so. Not very practical, or logical. Hence the easier option of locally switching to BST (which itself is GMT +1) for the daylight savings period, and switching back again when that adjustment is no longer needed.
The confusion over all of this is also why GMT is largely replaced now by UTC (Co-Ordinated Universal Time), which despite some jargon type technicalities, is basically the same exact thing, on the same timescale, just with a less area specific name attached.
