Im not sure that the original post was aimed at including Franchise agreements, or UK airlines filling in gaps such as TUI or TCX when their European counterparts need extra capacity. It is more scheduled operations being operated by the UK carrier - so let's just go with their own flight number and being operated on a British registered aircraft therefore removing the likes of Sunair etc.
Easyjet - yes
BMI - yes
Eastern - yes
Flybe - not yet as their SAS flights operate with SAS numbers but when they open their DUS base it will be BE all the way.