David Cameron has cautioned Vladimir Putin against ripping up the international rulebook by destabilising Ukraine and promised to warn the Russian president of the long-term economic consequences if he pursued this course when the two leaders meet at the G20 summit this weekend in Australia.

It will be the first meeting between the two leaders since the Ukraine crisis erupted. It is also expected that Barack Obama will hold a bilateral with Putin at the summit. Putin was debarred from a meeting of G8 leaders in Wales earlier this year in protest at the Russian invasion of Crimea

In his set-piece foreign policy speech at the Lord Mayor of banquet in the City of London, he warned his business audience that Britain’s economic security depended on its national security, adding: “Russia’s illegal actions are destabilising a sovereign state and violating its territorial integrity.”

He said Russia was “ripping up the international rulebook and disregarding the democratic will of the Ukrainian people to determine their own future. This weekend has seen further shelling, and reports of more heavy weapons moving from Russia into south-east Ukraine.”

He added: “There will be those who say that this isn’t our business and that we shouldn’t interfere. And some will argue that we can’t – that we have no influence to bear. But I believe both views are wrong.”

He acknowledged that no military solution was available, but said “economic sanctions on Russia are having an impact. Capital has flown out of Russia, banks are short of finance, and the Russian stock market and Rouble have fallen significantly.”

He said that Russia’s actions posed a grave danger to the rest of Europe, adding that Britain should not need to be reminded of the consequences of turning a blind eye when big countries in Europe bully smaller countries.

Although the former Russian president Mikhail Gorbachev has said that the world is on the brink of a new cold war, Cameron said this was not the outcome he sought and nor was it inevitable.

But he promised he would tell Putin at the Brisbane summit that if “Russia continues on its current path, then we will keep upping the pressure and Russia’s relationship with the rest of the world will be radically different in the future. Of course there will be those who will argue that we should just draw a line under what has happened and that our own economy will suffer if we don’t. But they are wrong.

“If we allow such a fundamental breach of our rules-based system to go unchecked then in the long run we will suffer more instability and ultimately be worse off as a result. So once again Britain’s engagement is not just morally right, but also in our national and economic interest.”