This will depend on the circumstances of the case. In the event that both parties are in agreement to divorce then, costs will be kept low. However, should one of the parties not be in agreement or be difficult, the process could become protracted which will in turn increase costs.
The solicitor will likely charge an hourly rate so costs will depend on the level of seniority of the solicitor you will be instructing and you should check with the solicitor at the outset as to what their likely estimated fees will be. You will need to pay a court fee of £550 to accompany the petition to the court.