Has Brexit harmed UK trade? [pdf]

Their argument is independent of inflation because they are comparing relative exports to EU and non-EU. If there was a Brexit effect that distribution should have shifted but it didn't.

But they do take inflation into account and it shows the opposite of the predicted effect:

If we exclude precious metals, then exports to EU destinations increased by 13.4 per cent while exports to non-EU countries increased by only 5.7 per cent (see table 2), and if we use deflated data then exports to EU countries fell by 7.2 per cent but decreased by 9.8 per cent to non-EU countries (see table 3)

(precious metal exclusion is standard in this type of trade analysis)

The OBR's claims are full of severe flaws, with problems like key numbers just being made up, extreme assumptions that were already falsified, or relying on averages of economic predictions made by publicly Brexit-hostile organizations, years before the exit process actually happened and which didn't reflect the final agreement. The OBR very clearly chose a position and then made an analysis to meet that goal, which is typical of most of the British civil service's institutions in their approach to Brexit.

This analysis in contrast is very careful to study the different factors impacting British trade in detail, in particular reallocations due to new rules of origin accounting that don't represent real trade differences.