The date of Brexit at present is 29th March. One worst case scenario is that all aeroplanes entering/leaving the country are grounded. I think it's unlikely but it has been discussed in the press https://www.theguardian.com/business/2017/mar/09/brexit-airl...

You'll probably be fine as a tourist but as I said, it's the uncertainty that's the problem. If it were me, I'd leave a week or two before 29th March.