I did it two summers ago at Gatwick (I assume you're flying from there?) and it was really easy - no fuss, no queues and an easy service.
I just checked the BA website and it says this:
What is the London Gatwick early check-in service and how does it work?
Answer
Customers departing on British Airways scheduled flights from the North Terminal at Gatwick can check in, deposit baggage and collect their boarding cards the day before their flight departs.
Who can use this service?
The service is available for customers travelling on any British Airways service departing before 15:15 the following day.
Self-Service check-in details/Self check-in process
Early check-in is available between 16:00 and 22:00 on the day prior to departure for those passengers qualifying as shown above.
To use the service, present yourself, your documents and your checked baggage at the British Airways check-in desk as though you were about to travel. For security reasons, we can only check in customers who are able to attend in person.
You will be required to provide a telephone contact (preferably a mobile number) at the time of check-in.
Please note: once checked in, we will not be able to retrieve your baggage.
Day of departure process
On the day of travel, you can go straight through security and to your allocated departure gate. Remember to be at the gate at least 45 minutes prior to scheduled departure time for intercontinental services and 30 minutes prior to departure for European and domestic services.
Have a Great Trip!!!!