If you enter into a new relationship, and you continue to keep in touch with an old BF or GF, then it is like saying to your new BF or GF, "I don't really love you - I really want to be with this other person".
Even if you want to be with the new BF/GF, this is what they will think. It's a matter of Love and Respect for your new partner that you severe old relationships completely.
That's my opinion :)