A family member switched to LHR from LCY when BA pulled the LCY-Copenhagen route, but that was because there was no alternative. You've been given the same route, just another day, so I doubt the commercial policy to applies to you will allow you to change to LHR. I've just checked and many of the policies say 'Same Route'. Really depends if BA are willing to consider LHR/LGW and just LON. Worth a try.