I'm seeing two common mistakes by commenters trying to analyze the Brexit vote shock:
1. Assuming that monetary offset applies to real shocks
2. Assuming that a cut in the BOE's target interest rate represents an easing of policy.
It turns out that these two errors are interrelated. The Bank of England has a dual mandate, which includes 2% inflation in the long run, but macroeconomic stability in the short run. It's probably easiest to view this as keeping NGDP growth steady in the short run, but gradually nudging it up or down in the long run to keep inflation close to 2%.
To make things simple, let's define AD as a given level of NGDP. Then the BOE wants stable growth in AD, at roughly 4%/year. Now suppose there is a nominal shock. In that case, the BOE should adjust policy to keep NGDP growth stable. If we use the Equation of Exchange:
MV = PY
You can think of that as the central bank adjusting M to offset changes in V. If you prefer a Keynesian approach, you can define the Wicksellian equilibrium interest rate as the rate that keeps NGDP growth at about 4%. If the Wicksellian rate falls (as it did after Brexit) the BOE will cut the policy rate, to keep growth in NGDP stable.
But monetary offset does not apply to real shocks:
When the AS curve shifts left, the BOE will keep monetary policy stable by keeping the AD curve stable (more precisely the growth rate is kept stable.) So real shocks will reduce RGDP, even if monetary policy is fully offsetting shocks that might impact AD. Monetary offset is a useful concept, but can only do so much.
I think people tend to overrate the importance of central banks in setting interest rates. The BOE is constrained by its macro targets. Thus 90% of the time when it adjusts interest rates it's not a true policy change, it's just the central bank reflecting a change in the Wicksellian rate caused by some sort of shock. It looks like the central bank is what's causing rates to change, but that's a cognitive illusion.
As an analogy, a bus driver will adjust the steering wheel on a twisty road. Superficially it looks like the bus is moving around at the whims of the driver. But a deeper explanation is that the path of the bus reflects the shape of the road, and the driver simply adjusts the steering to keep the bus centered on the road. A true change in "bus driver policy" would be a change in steering that drove the bus off the road.
Central banks mostly adjust rates passively to accommodate changes in the economic road ahead. Occasionally they do something wild and crazy, like not adjust the interest rate to changes in the Wicksellian equilibrium rate. How do we know when that happens? The economy goes off the road. NGDP goes wildly up or down. The last good example was in 2008, when rates were cut too slowly. Another example is the 1970s, when rates were raised too slowly.
When big mistakes are made, the problem is almost always "rates adjusted too slowly."