I'm not certain, but there's a strong possibility that it's When the Gangs Came to London by Edgar Wallace (1932), whose full text is available on Project Gutenberg.
Machine-guns in Park Lane:
He waited on the opposite corner of Park Lane. At three minutes before the hour Salaman arrived in his chauffeur-driven car and stepped down on to the sidewalk. [...]
A middle-aged man, wearing a flaming flower in his buttonhole, was walking from the direction of Piccadilly. Terry saw him stop and look at his watch and then go on. He walked a short way past the spot where he had to meet Salaman, then he turned back and came to a halt within a foot of the position which had been described over the telephone. Salaman had seen him and strolled down to meet him. They saw the man touch his hat and ask Salaman a question, and the young man took an envelope from his pocket and handed it to the messenger. As he did so, the detectives closed. They were within a foot of their terrified prisoner, when the staccato crash of a machine-gun came from somewhere overhead. The little man with the flower in his coat and Salaman went down together. A detective drooped and sank by the railings, and a second a doubled up and fell with his head in the roadway.
'In that block of flats!' yelled Jiggs. [...] 'One empty flat? That's the place. Have you a pass-key?'
By the greatest good fortune he had. But there was no need for a key: the door of the flat was wide open, and even as the men ran into the room they could smell the acrid scent of exploded cordite.
Jiggs ran into the front room. The window was wide open. The room was empty, except for a chair drawn up near the window-sill and the small machine-gun that lay on the floor.
An aeroplane attempting to drop bombs on Cavendish Square (not Barnes Common, although the latter is mentioned elsewhere in the story):
'Yes, an aeroplane.' [...] The roar of the engine was plainer now. The machine was coming straight for Cavendish Square. They looked up, but could see nothing. Then suddenly it swept into view: a small, black plane, flying so low that its wheels almost skimmed the roof of a high store building. It dipped a little, came straight towards the northern side of the square. It swept up, turned, land came back. 'Looking for the lights,' said Jiggs. [...]
The plane was nearing the centre of Cavendish Square, when it suddenly heeled over. Its tail went down and it fell with a crash in the centre of the garden which occupied the middle of the square. [...] 'What have I done?' said Jiggs. 'I've shot down the man whose job it was to bomb Mr. Cuthbert Drood, and who would have bombed him if he could have found the red lights that had been put there to mark the house. These guys have got other ways of killing besides automatics!'
The police who jumped the railings of the square found a groaning man amidst the wreckage. They found also a hundred-pound bomb, which was subsequently discovered to be packed with alanite.
I can't find anything about a gas attack, but several scenes of the story are set in Leslie Ranger's West-End flat.
The only mention of a yacht is that Cuthbert Drood "hunted all the winter and yachted most of the summer", but there's an artillery battle with boats in the Thames (not the Solent):
A policeman leaned over the parapet, saw a long launch heading for the centre of the river and challenged it. There was no answer. He pulled a revolver from its holster and fired twice. Almost instantly there came from the dark waters flickering lines of intermittent light and the stammer of a machine-gun. Bullets sprayed the parapet, smashed a few windows, but did no other damage.
By this time the boat was in mid-stream. The watchers saw again the flicker of machine-gun fire and heard the rattle of it. In mid-stream was a police launch, and the battle was one-sided. By the' time reinforcements came the launch had disappeared.
It's not a perfect match, but it seems a little too close to be coincidence. I did find some other books of Edgar Wallace which also have some of the elements Sayers described - e.g. The Terror has a gas attack, although not by the CID and not on a West-End flat, and mentions Park Lane, Barnes Common, bombs dropping, and machine guns - but this one seems by far the closest. It also fits the context of Sayers's discussion since it's a work of detective fiction. Perhaps she was conflating more than one different story in her head (this sometimes happens even with people asking story-identification questions on Stack Exchange: they remember bits of more than one story and answerers have to tease them apart).
For the record, I found this story by the following web search:
"park lane" bombs "barnes common" guns yacht solent.