I think we are talking two different things here.

First off, there's the question of leaving the country. As I understand it, the airlines, including BA, have agreed to ask the question as to whether the trip is for business, but not enquire further. Rumours are that the Home Office will require a form from 8 March, but nothing has been published yet.

And then, there's the need to check that the passenger is allowed into the foreign country, and that will vary depending upon the country, the date of travel and no doubt the phases of the Moon. But I believe that they still use TIMATIC for that. The problem, of course, is ensuring that all the pieces of paper that are required are the correct ones, and correctly filled in.