OP I'd gently remind you of a flyer talk rule that thread titles should be meaningful so people can understand what you are asking help with.
Your question is basically 'do I have to book BA flights via BA.Com if I can get them cheaper elsewhere?'
To which the answer is a resounding 'no'. You can book via anyone you like whether it's another airlines website e.g. I';ve booked BA flights using the AA website) or a travel agent - again I've used expedia.
However booking direct does offer some additional benefits such as
~ If a flight gets cancelled or rescheduled in advance if you book via a travel agency then you have to deal with them to sort the situation out and that could take longer. Booking direct means you deal with BA direct and may have a wider range of options available such as reroutes.
~ You may not earn avios and tier points as the ticket sold by a travel agent may be a special fare where you don't earn. (mind I booked a BA flight via AA but with an AY codeshare and AY does not give a status bonus avios so that cost me 3k avios)
~ Booking direct means you get protection of the 24 hour cooling off period for a full refund should you change your mind. Booking via a travel agency may mean that whilst you could cancel with a full refund from the airline the agency may still charge you an admin fee that the airline doesn't.
Now in the scheme of things these issues don't affect or bother the vast majority of travellers (very few flights get cancelled and the majority of people don't collect miles). But they do bother some. And some people would rather pay a little more to book direct than save some money by booking via an agent.
The choice is yours.