Now, in my training with BA, there was no such test.
It's absolutely beneficial to be a good swimmer, but if you're able to doggy-paddle your way around, that's fine. Don't let it put you off. Let the trainers decide whether you're a good enough swimmer.
There were a number of people on my course who struggled. Particularly with the life-vest on. You are allowed to have someone help you, too.
Most tricky part is getting in to the life raft but again, help will be offered if you absolutely, totally can not manage it.
DO NOT LET YOUR SWIMMING ABILITY, or lack thereof, PUT YOU OFF APPLYING!