I had a good experience at Beatrice's. The place is convenient for O2 arena, you can even walk there with a 30 mins walk mostly along the Thames. It has good transport connection with buses and Thamesline trains. Greenwich is a lovely place and would recommend it if you prefer a quiet place to stay. It has lots of things to do and visit. Lovely restaurants and café. I've never felt in danger, not even walking back at 2am.
Beatrice is very nice and welcoming. There was an issue with bathroom sink and because it was not possible to solve it, she gave me a discount. I really appreciated that, because I did not request it or expect it.
The room is spacious and luminous. It can bother those who needs total dark to sleep. Bed is big and comfortable. I've slept well since day 1.
As it is clearly stated, you share the house with Beatrice and her 2 children, therefore I would recommend you ask her about their morning routines so that you can adjust and plan the use of the bathroom without issues. I had no problems at all.