It sounds a bit like too many parties are involved here - consultant (whatever they do), BA (as the issuer of the avios) and CX (as the partner airline).

If you are now dealing with BA directly and BA have accepted responsibility for rectifying this, then that may make things easier. I would however make sure that you get something definite in writing from BA saying that they will do this name change.

The reason I say this is that name changes on BA are a real No-No. Unlike some airlines, BA will not change a name for a fee (say for someone else to fly) or often to correct names say when first and last names have been transposed. Change of name due to marriage (with a marriage certificate) is allowed. Errors by BA agents will also be corrected.

I say this as the use of an agent complicates matters. How could agent access your avios with the wrong surname? If it is the agent's mistake, how quick were they going back to BA? Was this in a jurisdiction that has a 24 hour cooling off period for telephone bookings? Does that apply to agents? Was it reported in that time?

I say this because BA are very strict on name changes and it sounds odd to me that something that will require manual intervention to override blocks on name changes (and quite probably reticketing) is just in an automated queue with far more straightforward changes.

I may be overly pessimistic, but I would want some assurance that BA are definitely go to action this, even if it will take some time and may not be done until nearer the flight.