Do UK police have an obligation to enforce the law?

No, not really. This parliament link http://www.parliament.uk/briefing-papers/SN04230 says "There is case law to suggest that, although under a general duty to uphold the law, chief officers of police retain discretion as to the degree of effort they will attach to enforcing any particular law at any particular time.

The discretion possessed by the police in enforcing the criminal law was considered by the Court of Appeal in the case of R v Metropolitan Police Commissioner, ex parte Blackburn (1968)"

Ultimately, any attempted prosecution would have to be in the public interest. An example of this would be, everybody knows that it is illegal for someone under the age of sixteen to have sex, but if a 15 year old and a sixteen year old were to have consensual sex prosecution would be highly unlikely. This is because it just wouldn't be in the the public interest.

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In the United Kingdom the police's main purpose is to enforce the law. That is the sole reason why they were created.

Other methods that they use to "keep the peace" have evolved over the last couple of hundred years. For example some police forces and some individual policemen exercise discretion and give warnings when they could actually effect an arrest and prosecution. But that is a discretionary power and should never be taken as evidence that the police are not obliged to enforce the law.

There is some evidence that in a few other countries the police force exist primarily to protect the resident political regime. This is not always the same as maintaining the rule of law, but it usually maintains "order" by some sort of fear or force.

Our view of the US police forces is given by the television programmes and Hollywood films. I really hope that these stories of policing methods and the individual "cops" are not accurate. If they are then you Yanks deserve our sympathy.

Well damn, I guess us yanks as you call us don't have a right to speak since you are all high and mighty and such. I guess the genocide of the Cellts and the oppression that goes on today doesn't happen as well. The truth is we don't have the corner of corruption, even though I will admit our government does more than it's fair share both to our citizenry and abroad.

In short, yes, the police in every country have a duty to enforce the laws in their own jurisdiction within their own borders. The fact that police departments and governments worldwide shirk this responsibility regularly does not make it any less of a responsibility.

Where do you get the idea the US police can ignore the law?

A few stupid hicks will claim this, but the books are filled with laws which are there specifically to make police officers and bureaucrats comply with the law code. You'll find that every local cop who boats they wont' be complying with a particular law is actually just a politician, who says this in public to get votes.

well of coarse they can not just ignore crimes when they feel like it but that is not to say they must get the force helicopter out because some on stole the Vickers bike.

in other words just because you might feel they are not doing enough does not mean they are not

if your not happy with how the police have dealt with you then make a complaint

Within reason they can use their own judgement but for serious offences no they can't.

Simon's answer is correct.