The thing to do would be looking up low flying prosecutions for some case examples. Most of these come after a pilot on the ground reports an aircraft low flying since non pilots have no knowledge of the rules, or how low something actually looks. The last one I read I seem to remember was low flying over a football stadium, possibly Manchester. In the court case the expectation was on the pilot to provide evidence of which field he would of actually used had an engine failure occurred, and football pitches and playing fields were not acceptable. They even had photos in the report of the field the pilot elected, which was then deemed not to have been suitable and the pilot was fined by my memory.
Not sure how they would view using the river itself, not sure there is any case law on this.
The caa only seem to push for prosecution if they know they will win, looking at the prosecution lists each year it is rarely just low flying, but also compounded with no medical or insurance, and they just get them to plead guilty to one of them.