OP, your past will influence your opinion on what you saw yesterday, and your perception of risk.
If you'd spent your whole life in the UK, I'd say you were being daft.
In many places though, the police are a visible sign, enforcing a brutal/chaotic government outlook.
It's easy to look at the policing of demonstrations, and say 'agghh, the beginning of an oppressive approach to population control'.
The danger does exist, we are not so special; and saying 'it couldn't happen here' is ridiculous.
But look at the love for Corbyn. People are free to express that, and as things get more controlled, people are taking to the streets more.
Many conservative politicians would turn away from May, if only to increase their own chances in the next election.
While that sort of privileged, money-centred, politicking still exists, we are safe enough.