My memory of company law isn't as good as it was but if over 3% of shares are held by a person / company I think there are various additional rules to be followed in declaring one's stake; below 3% and one can be a little more anonymous publicly.
It is likely that BA still hold some shares in Flybe, even if it is worth just a thousand pounds - this will allow BA to send someone to the company AGM and listen to proceedings if they wish.