If interference took place then it's likely that they pushed both Leave and Remain in order to generate as much discord as possible. It's apparently something they did in the US and it would make sense to do so as it's easier to engineer direct conflict between both sides when you're manipulating both.

The debate over Brexit is damaging enough on its own so even if Remain had won it would rage on and continue to hamper political discourse in the UK. Look how much of a struggle it is to do much of anything at the moment. If there is a Kremlin-backed campaign to weaken Western countries then they don't even need the UK to leave the EU, all they need is for the UK to descend into constant bickering and cease to function efficiently.