There is no need for it to be done at check in. BA and most airlines allow you to submit that info in advance - either using VeriFLY or their website.
We used VeriFLY when flying to LHR last month and had no wait at check-in where they saw the tick and just printed the boarding passes.
The E gates are now able to match your passport to your PLF. the delays come about when there are lots of families (as under 12 cant use the egates) or when the system goes down (which seems to be a weekly occurrence at the moment). We had this and it took around two hours from landing to exiting baggage reclaim.