You had good advice from Twilight....go over to the ovarian posting room and get some real first hand advice from those who have been where you are.
But to answer your question, no they won't do a hysterectomy per your request. I know that first hand....I had to wait until my uterus was falling out until they would do that for me. Good luck dear.
I don't know how elective hysterectomies go over with National Health in the UK, but here in the States it's not all that common. I see from your profile that you are 32 years old, and most docs over here wouldn't want to sterilize a woman that young without a major medical reason. Of course, the insurance companies would want a better reason than a relative having cancer before they would pay for the procedure too.
I wish I had some words of wisdom for you, but your situation is so very personal and individual that only you and your doctor can sort this one out. I'm so sorry you lost your mum. :-(
I can understand your concern. If there is a strong family history of breast cancer or ovarian cancer, you should possibly be tested for BRCA gene mutations. If positive, you would be eligible for an elective hysterectom/bilateral oophorectomy.
c.
You should post this question in the Ovarian cancer forum. There are knowledgeable women in that forum that would know more about this than here in the hysterectomy forum :-)