It seems pretty clear that silent prayer was in fact the reason why Vaughan-Spruce was arrested:

https://news.yahoo.com/british-woman-arrested-praying-silent...

> When she stood in front of the building by herself, Vaughan-Spruce reportedly did not carry a poster, candles for a vigil, or graphic pictures that might be deemed disturbing to local residents, according to the video

> When officers asked whether she was part of a protest, she replied “no.” They then asked if she was praying, to which she said she could be doing so “in my head.” Police then searched her, and patted down her hair, before handcuffing her and escorting her to the station.

The article you link to talks about a different person, who was arrested for holding a sign saying "Praying for freedom of speech."