In scenarios where foreign countries operate intelligence on the soil of host country, no foreign intelligence would straight forwardly come up claiming it is us (dumb to do so).
True, if we understand your "intelligence" as covert intelligence. But "political influence activities" are not necessarily either covert activities or intelligence activities. Indeed, they are fundamentally political activities. It's right there in the term. Some such activities are among the primary duties of a foreign delegation. There is therefore good reason to suppose that Iran will register some political influence activities with the UK government.
In that sense, no law enforcement can simply march into embassies, what is UK trying to achieve here?
Basically correct. UK law enforcement technically could do exactly that, but they will not, because their own political leadership would not tolerate it. But it is possible to imagine circumstances in which that would change.
We have to speculate about the UK's actual objectives, but the effects are at least twofold:
by taking notice and making an official political response, the UK is sending a political message to Iran that they are displeased. The requirement they've placed is too minor to justify a strong diplomatic response, but it's a stage from which they can escalate.
by placing any requirement at all, the UK has created a political basis for taking action against anyone whom they find to be in violation. The most likely action (against anyone who is not a permanent resident) would be expulsion.
Iran can work through embassy to carry these alleged activities and still carry covert operations. Similar to source cited above, Irani intelligence, i.e. agents could seek asylum in ally embassies, hide in let us say, Lebanon embassy in UK and carry these operations.
That an operative found to be in violation might hide or otherwise attempt to avoid being apprehended by UK authorities is largely moot, because doing so after having been detected would not well serve either their operational or their underlying political objectives.
Note also that the referenced article's comments about UK police arresting Iranians over threats to national security seems to be a non sequitur. There is no indication that the UK would consider failure to comply with the new policy to constitute a threat to national security, and it's unclear whether the UK would attempt to arrest anyone believed to have violated the new policy. The policy does not, itself, appear to create a basis for doing so.
My question is, if at all effective, what is UK trying to reduce here? Intelligence services won't simply come up to UK and declare themselves openly as politically inducing agents in the country.
You've got that mixed up. Nothing here is about "politically introducing agents in[to] the country". Of course intelligence services enjoy some amount of support from their countries' embassies. Of course some embassy staff are covert intelligence officers. And of course the embassies, services, and operatives don't admit to any of that. Everyone recognizes this.
In addition to the effects already described, the UK probably hopes that this action will influence Iran to reduce covert political influence activities in-country, and / or to adjust the operating parameters of such activities in ways that make them less effective (in order to better evade detection).
