By fact I mean some true evidence or some proof, something that can be
taken as a proof in some sort of International Court of Justice, like
- people who organized this attack, their motivation to perform the attack and so on.
There is no such thing as an International Court of Justice for this kind of incident (there are ad hoc war crimes tribunals established for whole wars, as well as a less ad hoc International Criminal Court that does basically the same thing, and there is an impotent International Court of Justice that pretty much limits itself to boundary disputes).
In general, disputes between sovereign nations, and particularly those involve alleged hostile action, aren't subject to the same kinds of rules of domestic criminal justice. It is often much easier to determine which government is responsible for hostile action than to determine which individual did it. But, that's fine, because nobody is trying to hold the individual responsible, only the government that authorized the action.
To start with, disputes between sovereign nations are inherently about collective, rather than individual, responsibility. The perpetrator may have been acting lawfully pursuant to lawful military orders by the standard of his home country.
Equally important, decisions made by sovereign nations about violations of treaties or legal standards aren't made in courts, they are made by heads of state and senior executive branch government officials. These are violations that must be responded to in time frames inconsistent with the slow, bureaucratic criminal justice system that is available when a government has total control over the defendant and the overall situation. Instead, they are good faith decisions made based upon credible evidence.
This is the only way to secure accountability in an imperfect world.
In this case, the very unique method of the killing which is singular to the Russian government, the identity of the victim, a history of past similar incidents by the same perpetrator, and ominous pronouncements short of a confession by official media, together are a clear enough indication to justify action by the UK Prime Minister and cabinet officials (e.g. expelling 23 Russian diplomats and imposing other sanctions) without serious risk of being found to have been mistaken later on.
A similar process was used to justify a retaliatory strike against the Syrian regime by U.S. forces for chemical weapons usage.
Mistakes are made in this mechanism for truth finding in disputes between sovereign governments which can be catastrophic. The most obvious case in point was the Iraq War which was based upon false allegations. But, out of necessity, this is the epistemological foundation of international decision making.