"We can keep this place if you like." It was a descent flat, certainly. And with any luck, post-Lord Cheeseknob, the property values in Diagon would skyrocket. Keeping the flat made perfect sense. And it even gave Sirius an idea, which hit him like a bolt of lighting and he sat up even straighter beneath her.
"Ooh! And you know what? Remus could live here. Properties always maintain better when there's someone living in the space, and he needs something stable. Something..." Sirius hated to say it, but this was him and Em. Whatever he said would never be repeated to another soul. "He needs something free, basically. It's a perfect arrangement."
Sirius and Em would sell the Clapham flat, buy a house in London, and ask Remus to watch after the Diagon property. And if he really, really needed to, he could get a job.