Schedules for August remains as a placeholder for most airlines so there is no guarantee that a flight that you book at this moment would operate.
TAROM ( direct ), Lufthansa, Austrian, Swiss, Air France, Turkish Airlines, etc... all fly both to London and to Bucharest ( at the moment ) and I would consider them safe. Although your safest bet would be Wizzair and Blue Air which are LCC's.

BA plans to resume Bucharest on 5 July 2021 and unless there are further travel bans, they would be most likely operating that route in August.

Also a reminder that, if the current guidelines stick when you travel, you would need to self-isolate upon arrival at the UK for 10 days ( 5 days + test out is possible ) as Romania is in the amber list of the UK. For reference, at this moment, the UK doesn't have any exception for vaccinated travelers.