The birth Sun Sign you seek is determined by the position of the sun in the heavens as seen from Earth at the point in question. The sun does not pass from one sign into the next at exaxtly midnight (either GMT or BST) very often. The changeover point can be found in a table called an Ephemeris. You can download a free one from
http://www.achernar.btinternet.co.uk/fm.html
and then choosing the year in which you are interested.
For example, if that baby was born at 00:00hrs on 20th February, 2003 then, according to the Ephemeris for this year "Th 20 09:58:05 00PI55" the sun was 55 minutes of arc inside Pisces (each sign is given 30 degrees). This is for GMT at Greenwich in London, and as we in Britain were on GMT in February no correction is required. However, a correction will have to be made for the location east or west of Grenwich.
The sun travels once around the earth in 24 hours so 360/24=15 degrees per hour. If the baby were born in, say, Liverpool then this was 2 degrees 58 minutes west and its equivalent sidereal time (11 minutes 52 seconds) must be subtracted from the Ephemeris Sidereal. 12 minutes is 0.0083 of a day, and the sun traversed from 29AQ55 to 00PI55 in this time, that is one degree of arc and .0083 of a degree is 0.5 minutes of arc. So this midnight Liverpool baby was still inside Pisces by 50 minutes of arc.
For the bah humbug brigade, all I have described is part of a method of casting a Horoscope, an astronomical figure set for a given time and place. It does nothing more than purport to show the position of the sun and planets against more distant stars at a set time and place. With that you cannot argue, however, the interpretation of that data, is open to endless discussion!