Maybe Mary can't return to Britain? We don't know for who she worked in the Great Britain, but we think that she was a part of MI6. The BO is also an international organisation. Maybe something happened in the Great Britain that Mary had to leave it ASAP, and that's why she couldn't return there and decided to stay in Japan?
From my perspective, Tsutomu told his family to go to Japan for safety while he acted like a fodder for his family. This way BO's attention would go to him, not his family anymore. That's one kind of expected psychology you would think.
Mary going to Japan, for the second time (after Tsutomu told her) is not a confirmed course of action. What I initially thought is, she might have known that the scientist Shiho Miyano is alive, and is in Japan, so she would want to meet with Shiho to get back her adult form or something like that. How does she know Shiho is alive? We don't know for sure if she 100% knows this, or that she does, but Gosho hasn't revealed to us just yet. She has only asked Sera to go around and search for the antidote, and it seems Sera doesn't know that Shiho is alive right now either, so I think, Mary doesn't quite know Shiho is really alive at this point in time. A more convincing reason would be that there are allies in Japan like you said, that could help them out better. But even then, they still have to move from hotels to hotels a lot, so it doesn't seem like there's someone protecting them right now.
Above all, right now, I DO THINK, that Mary is looking for the bodyguard Asaka, and thinks, or knows very sure, that Asaka is still alive, based on the fact that Asaka is missing. Why? Again, we don't really have clues at this point, but judging how the Kouji case went, it's possible that Asaka at least knows Kouji, who already knows the Akai family, and so Mary knows Asaka to some extent as well. She probably heard from some source that Asaka has fled to Japan or something like that. As victims of Rum, they sure understand each other's situations. Tsutomu was most definitely DIRECTLY involved in the Kouji case before, based on HOW Subaru said to Conan. Thus, Tsutomu knowing who Asaka was at the time could be something that tells him, that making his family to Japan is a correct decision to make. I do think, that Tsutomu could trust Asaka to a great extent, and know that Asaka is on the good side (BO spy, BO traitor, or merely a secret agent from some unknown agencies). Getting into contact with Asaka, could very well help Mary look for good info from BO (assuming that Asaka knows enough of BO, is a former BO member, or a spy like Kir, etc), to locate the data of the antidote and such.