Muslim Divorce

Yes it is necessary.

Although consideration for Khula is essential, the actual release of the dower or delivery of property constituting the consideration is not a condition precedent for the validity of the khula. Once the husband gives his consent, it results in an irrevocable divorce. The husband has no power of cancelling the ‘khul’ on the ground that the consideration has not been paid.

HUSBAND deserted the wife as a khulla.

A Woman, Under Islamic law of KHULA, may initiate a divorce against her husband as follows:
Khula' is when wife has a dislike for her husband and ASKS HIM to divorce her in exchange of a sum, or all or part of her MAHR. In such a case, when the husband agrees to divorce, he forfeits the power of revocation, except when the wife agrees to take back the money or ransom she gave. It is not permissible for a woman to seek divorce from her husband unless she has borne ill-treatment from him or unless she has an acceptable reason which requires their separation

From the above it is clear that without the consant of husband Talaq under the Khula is not possible.