Perhaps a heck of a lot of creative accounting was used to make it look like the govt was spending a fortune when it wasn't
A lot of money was spent, we are one of the six thousand companies asked to prepare, and had to complete a number of government white papers on readiness due to impact if we had not. It takes a shit load of civil servants to collate and understand the feedback.
I can see how it ran into billions, from medicine stock builds, civil servants, thousands of pieces of new legislation need to be created,warehousing space, processes for things like visas and transportation, importation of goods, even things like new invoicing and vat processes on imported products, how to pay the customs duties that never existed before, staff to manage it, armed forces preparations, new security processes, the list is endless. Even websites with an eu domain owned by companies in the U.K. would have went down at the point of departure.
Much of it is unseen by the british public but I can see how it easily reached this sort of level of spend. And then some.