Unfortunately, the headline is a bit misleading. NGDP (left scale) grew at a 5.0% rate in the first half of 20172016, and a 4.6% annual rate in the 2nd half of the year.
James makes a mistake that I see quite often, using data before an "event" in an event study. He uses year over year data, which includes a 6 month period before the Brexit vote. It doesn't seem likely that the Brexit vote in late June caused rapid NGDP growth in the first half of 2016!
Nonetheless, even a 4.6% NGDP growth rate is reasonably impressive---above the average NGDP growth rate of the last 5 years. Thus James is right that the BoE policy of monetary offset was effective. We'll need another 6 months before the YoY data will consist of only data collected after the Brexit vote.
He's also right that many critics of Brexit predicted a collapse in aggregate demand after the vote:
Anti-Brexiteers were all forecasting a collapse in AD following the vote. It was never clear if this was going to come from shocked consumers spending less, from dramatic falls in business investment, or maybe both. Nothing of the sort happened, as we now know. All those top economists and other experts were completely wrong.
But not all anti-Brexiteers expected a collapse in AD. The steady growth in AD (so far) is consistent with the market monetarist model.