The OBR did not make the claim in such terms. The OBR posited a lower rate of growth in productivity after Brexit, which would translate into lower GDP growth. A problem with productivity has occurred, and indeed a fall in productivity, not just a fall in its rate of improvement: this was due to Covid-19 and is concentrated in the public sector, which does not trade with the EU.
As John (now Lord) Redwood has explained, the OBR report was a forecast based on the unproven assumption of a lower rate of improvement over 15 years in UK productivity, of ¼ per cent per annum less than if the UK had not left the EU.
Those who use the figure are unable to explain either the timing, cause, or materiality of the supposed drop. The 4 per cent has been discarded in favour of the more dramatic 8 per cent, not least because we are seven years into the lifetime of the OBR’s forecast (2019-34), Covid-19 has intervened, and it is not possible to track whether Brexit alone has precipitated changes in the rate of UK productivity growth.