The referendum on Brexit was almost two months ago (June 23). We are now far from the recession that was announced in the case of a “Leave” vote. Yesterday, retail sales for July were strong (+1.4%). It is not a fracture (see this article this morning in the Guardian).
But it is too soon to rule out the possibility of a recession.
The main reason for that is that no measures have been taken to change the rules with the European Union.

Economists said that two points were important to eventually create a slowdown that could be transformed in a recession. The first is the access to the single market and the second is the European passport. The first will change trade rules between the United Kingdom and the EU. The second is the specific rule that regulate EU companies’ business  within the EU.  Nothing has been done on these issues and we don’t know when the notification of Article 50 will be done. As far as no measures are taken that could change the rules between the United Kingdom and the European Union nothing will happen. As no one knows what will happen for these two points, there is no change in behavior.
People have negative expectations in July (see the Markit survey for companies and the GFK survey for households) but they have no reason to change their activity yet.
Moreover, the Bank of England has decided to adopt a more accommodative monetary policy that has push down interest rates to their lowest level ever. This could boost activity in short-term. At the same time, the drop in the value of the pound has created incentives for tourists to visit the UK this summer.
The real change will come with the notification of the Article 50 and the start of negotiations with the EU. Rules will change at this moment and UK will have to find a new equilibrium which will not allow a large deficit of its current account. This latter was accepted as far as UK was a EU member,  but some adjustments will be needed. This will be part of the new equilibrium. It could be less enthusiastic.