(assuming you used GPL v2; I have not read GPL v1).
It states clearly that in lieu of any modification of any GPL v2 work (paragraph 2) by any party, that party is required to "...cause any work that you distribute or publish, that in whole or in part contains or is derived from [a GPL'd (v2) program] or any part thereof, to be licenced as a whole at no charge to all third parties under the terms of this licence." (subsection 'b')
So, provided your employers accept these terms, you can use your old GPL'd program code, modify it, release it under the original licence and copyright (acknowleging the owner of the modifications (your company)), and go home and merge it into your source tree, as per GPL v2.
If your employers do not accept the licence, you can't use your old program (because you are acting for your company, not yourself; the company does not own the work, you do, and they cannot make you change the licence it is released under, nor can they presuppose that you do, simply because you're working on it on their time) and must start, perhaps, from scratch.
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(assuming you used GPL v2; I have not read GPL v1).
It states clearly that in lieu of any modification of any GPL v2 work (paragraph 2) by any party, that party is required to "...cause any work that you distribute or publish, that in whole or in part contains or is derived from [a GPL'd (v2) program] or any part thereof, to be licenced as a whole at no charge to all third parties under the terms of this licence." (subsection 'b')
So, provided your employers accept these terms, you can use your old GPL'd program code, modify it, release it under the original licence and copyright (acknowleging the owner of the modifications (your company)), and go home and merge it into your source tree, as per GPL v2.
If your employers do not accept the licence, you can't use your old program (because you are acting for your company, not yourself; the company does not own the work, you do, and they cannot make you change the licence it is released under, nor can they presuppose that you do, simply because you're working on it on their time) and must start, perhaps, from scratch.
Good Luck.