In general BA will upgrade to Traveller Plus and Club ( generally not First ) to get staff away but they will not upgrade just because seats exist in that cabin although holiday spirits can often create more goodwill in respect of upgrades. As far as dress is concerned business casual is OK althought personally I always travel in at least jacket and tie just in case an upgrade is a possibility, and often appearance can swing it. I normally carry a single colour T-shirt and jogging bottoms in my hand luggage to change into on board if I do end up having to sleep in a smaller Economy seat.