I was in a similar situation,
Neighbor has an existing 2.75m extension. I applied for 6m, neighbor objected due to loss of light etc.
Reapplied with 5.75m (3m longer then neighbors), same objection but council approved as there was no more loss of light.
In my case, the sun rises at the front of my house, on my side, but sets on the back, on the neighbors side. so realistically no loss of light, but a gain of a higher wall in place of a short wooden fence.
Best i can suggest is if your not time pushed to get plans approved, and your architect is willing, submit 6m, if rejected submit a bit smaller...
You don't pay to submit, your only really paying for the time for architect to draw/submit, and time each one takes to apply and get a response.
May also be worth speaking to the neighbor and see what they may be happy with! After my objections, i spent time with the neighbour discussing the finish and agreed with them as to what they would be happy with... (assuming you want to stay in the good books with them!) eg a bodged brick finish as the builder had no access vs a nice clean finish as they had access and time to do the job properly, and clean up after themselves...