You can issue for "paternity testing" in Court and if the "father" refuses to attend, then the Court can draw an inference that he is the father. You will need to remove your partner's name from the birth certificate (if you haven't already) and explain to the Court why you did so - including showing the negative DNA test from your partner to the Court.

This sort of thing happens a lot - I'm a barrister and I see it often enough.

I'm glad you've seen a lawyer - s/he should be able to lead you through the paperwork and make sure it's all done "right". Good luck