World War I was triggered by a single assassination, but there isn't anyone seriously considering that option in this case. What seems quite a bit more likely is a continuation of the same tit-for-tat diplomacy of expelling diplomats and introducing new sanctions against Russian individuals and organizations that do business in the UK. There has been some speculation of the UK Goverment "appropriating" (or "seizing") Russian citizens' property owned in the United Kingdom based on the Criminal Finances Act of 2017:
The government could use the Criminal Finances Act, a law approved in 2017, to force Russians who may be implicated in the attack, or have close ties to Putin, to explain how they purchased property in the UK.
If they are unable to prove that the property was purchased with legitimate funds, it could be seized.
There is also increased attention to passing a UK version of the Magnitsky Act. The U.S. version allows freezing of assets for those suspected of being involved in human rights abuses which many would argue poisoning would qualify, but it's unclear yet on what exactly a U.K. version would include.
I would not expect there to be absolute beyond-the-shadow-of-a-doubt proof of anything any time soon, short of Russia admitting it. But that's more a statement on the nature of international intrigue in general.