Look what happened here.
Where's the spike in sexual assault figures from the arrival of the Zimbabweans as refugees around 1998-2003? The OMS estimates there are 110,000 people of Zimbabwean birth in the UK and most are comparatively recent arrivals (Zimbabweans in the United Kingdom).
Zimbabwe is a country with deeply misogynistic cultures, where men will call you to cross the road to them so they can sexually assault you without actually stirring their arse. Where a judge (white) released a man who'd murdered his wife when his dinner wasn't hot when he reeled in at silly o'clock, because "any red-blooded male would have done the same". Where rape of children is practically a national sport and another judge gave a man a suspended sentence for raping a 5 year-old... because it was a first offence. Its neighbour, South Africa, which is not identical but has a comparable set of cultures and does more analysis of these things estimates 40% of SA women will be raped in their life time.
I wish I were making all this up, but I'm not.
By your reckoning, there should be a huge leap in assaults on British women and children when the Zimbabwean refugees arrived, because they come from that culture. I'm absolutely sure some will have been involved in crimes of all natures, but (IIUC and I'm willing to be corrected on this), there hasn't been a noticeable leap in reports of sexual abuse.
In fact, here you are in 2016 extolling your continued freedoms despite living in a country with 110,000 Zimbabweans in it. You don't seem have needed the blocking of them to continue these freedoms.
There are very genuine issues to deal with, like the harassment in school described above, which need to be dealt with and not brushed under the carpet as that school did. And many of the issues will cost money, that can't be ignored either.
I also, personally, think there are systematic threats to women's rights and freedoms in the UK at the moment. But I don't think they're coming from 20,000 Syrian refugees over 5 years (or even 100,000). So I don't think not admitting Syrians will help. (I'm only using the Syrian example because I don't know what numbers you might be talking about from other countries.)