If you do not have status, then you can in theory, book those seats at 24hrs before departure by selecting them online via the BA website.

On selecting those seats, you'll get is an important notice about increased responsibilities of being seated at an emergency exits and the requirements and whether you agree to this. If you get on the aircraft and the crew determine you do not meet the criteria, then they could ask you to move.

I've not heard anything about having to physically check oneself in at the airport in order to get those seats.

However, those with status can select those seats anytime, so it's likely those seats will be grabbed long before then - I have an upcoming flight from SIN to LHR and selected one of those WT seats myself without any problems as I have status (however I hope I get a 89 GBP upgrade offer soon!).

There are 2x2 window/aisle seats at the very back of the plane, rows 51-53 (iirc), near the toilets. These are sometimes available at 24 hours prior to departure.