edit-local
As much as I can determine from this interweb thingy it is the transport company that is responsible for the 'verification'.
For air passengers the airlines will continue to send API information for departing passengers (and I assume the UKBF will collate this against the inbound API sent prior to arrival). The airline/ground agent will be responsible for the verification - and that process is not clear. Will they, as they do today, simply match the passport surname against the airline PNR data, or will they be required to match it against the API data (Names, Country, Gender, DOB, Document number, etc). If it's the former, it won't work. If it's the latter then add a minute or two per departing passenger.
The Sea/Chunnel companies will not be collecting/sending API for either arriving or departing passengers. But, on departure, their staff will be 'verifying' the documentation. Obviously not against API data but it's not clear against what they will have to make the comparison.
On a video clip on the BBC they showed a checkpoint at (I think) the chunnel. Car rolls up, driver collects and passes the passports to a staff member in a booth. (Booth is high enough up for both trucks and cars). Staff member verifies, but I can't see how without getting everyone to get out of the car. S/he can't possibly see and compare photos with all faces.
I think the UK voting population is being sold a pig in a poke.