Sorry, but I can't agree that vessel A is the stand on vessel. Vessel A is leaving the River Bure and turning to port into the Thurne. You should never cross the bow of another vessel, when not safe to do so. Neither is B the stand on vessel, as Coll Reg 15 says the vessel that has the other on her Starboard side, shall keep clear. Obviously the best course of action is for A to slow down and let B pass clear ahead. Under no circumstances where collision is possible. should you ever turn to port as one post suggests, this is strictly against the Coll. Regs. and whilst hirers may not know them, insurance companies do. If vessel A did turn to port and the other vessel knew the Regs, and turned to Starboard, a collision would still result.
When a collision is possible a vessel or both vessels must turn to starboard as required by the Coll Regs (Red to Red and it's safe ahead), then alter to the desired course once safe to do so.
The International Rules for Preventing Collisions at Sea, apply to Rivers and Harbours as well a the sea, unless altered for local waters by Governments, again as stated in the Coll Regs.
Having said all that, if I were vessel A, I would just slow down and let vessel B pass safely head.