Britain doesn't have a codified constitution and as such, every law, and every judge's interpretation of a law, defines the constitution as it stands on any given day.
Fact is, cops ARE the law - in any country, no matter how "democratic." They can - and will - arrest you at any given time in any given place for any given crime and if they choose to bust down your front door whilst you are watching telly - it's your tough shit.
Sure you can complain, you can take legal action if you want, but 99% of the time, you'll fail to get an acceptable result. Complaints get forgotten, letters lost and the independent complaints system of Scotland is not independent. The IPCC in England and Wales is deeply flawed. The police only investigate if it won't cost too much....appropriate to the alleged offence is there wording.
The bottom line is, I cross the street to avoid them and keep a solicitor's number in my purse. If you are in a high risk area, I suggest you write one on your forarm with indelible marker - they can't take your arm from you quite so easily....