Ah, harvey77, feel for ya girl! In more or less the same situation. Is your partner divorced? Where there access orders and or visitation rights set down at the time? This may help you, it did us!
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http://www.divorce.co.uk/legal/englandwales/le galcloserlook/children/orders/contactorder.htm
There can be an order for no contact but in any child matters the court treats the child's welfare as paramount.
It depends on the circumstances as to how long it takes, if it is contested, if reports are made etc...
There are other means such as an injunction. If there are serious problems they may be able to be held "ex parte" ie without the other person there or represented eg in domestic violence cases.
It's probably best to speak to a solicitor (some firms do free legal surgeries or a free first interview) and they can help you more on the costs and timescales and whether the person is entitled to any legal help.
There are also other places that can provide help and support if there are any issues of violence and abuse. If you ring the Samaritans (http://www.samaritans.org.uk/) they should have all the relevant numbers.
Hope this helps x