They compromised. They wouldn't have been able to travel together at all had they not established ground rules from the very start. In addition to the Doctor's first rule—The Master Can Not Attempt To Take Over/Destroy/Harm/etc Any Individual/Race/Planet/etc (ESPECIALLY Earth)—the Doctor, forever foolish and sentimental, also added rule twenty-seven: The Doctor Is Permitted To Take The TARDIS To Earth At Least Once A Month. Which was as excruciatingly excessive as it sounds, why do you ask?
The Master's first rule—from his secret list, the one the Doctor doesn't know about. The one written inside of his head. The one that is really more of a checklist to know when his time playing husbands with the Doctor should end and when the Master can go back to doing whatever he bloody well wants to—his first real rule is this: The Doctor Is Not Allowed To Act Like A Complete Idiot.
The Doctor is running around London (of course) with his usual manic grin that he saves for their visits to the Doctor's surrogate planet in particular. The Master wants to casually mention his most recent ideas of how he'd go about causing Earth's destruction. He wants watch the Doctor's reaction, see how that grin of his might twist and deform.
Up ahead, the Doctor turns back to make sure the Master isn't too far behind. He goes to grab the Master's hand like he used to back when they were children on Gallifrey. The Master allows the Doctor to brush his hand for a moment before he pulls away, lightly ignoring the Doctor's offer. He makes it clear that he won't run around with the Doctor, but he does pick up his pace a bit to help appease the Doctor's earnestness. Maybe the Master was not as subtle as he thought, if the calmer, gentler smile appearing on the Doctor's face was anything to go by.
Not long after, the Master mentally revised his first (secret) ground rule: The Doctor Is Not Allowed To Act Like A Complete Idiot Unless He Does So In A Grudgingly Endearing Way.
It looks like they will be playing husbands for a while.