Sir Andrew suggested Moscow may seek to exploit the ongoing row to strengthen its influence over Belarus and spark a diplomatic break in the continent.
Speaking to GB News, the former ambassador said: “The Russian aim overall is to absorb Belarus into its orbit and to rely on Lukashenko to do that.
“I think that’s a dangerous aim for them. But it is also dangerous for us.
“Another aim of both Presidents now is to divide and weaken European cohesion including that of the European Union.”
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He went on: “Which is barely strained anywhere at this time.
“So it is dangerous.
“At the same time, it is also as the polls have said in effect, a licence invasion of their country
“And the migrants are being used as weapons in that disruptive venture.”
Poland’s Prime Minister Mateusz Morawiecki has accused Vladimir Putin of being behind a migrant crisis at Belarus’s border with Poland.
He said in an emergency debate in the Polish parliament: “(Belarusian leader) Lukashenko is the executor of the latest assault, but this assault has a sponsor who is to be found in Moscow, and this sponsor is President Putin.”
It is believed that at least 2,000 migrants are stuck at the border in freezing conditions.
Belarus’s leader Alexander Lukashenko has denied that claims it is sending people over the border in revenge for EU sanctions.
For months migrants have been arriving at Belarus’s border.
Tension has been escalating between Minsk and its neighbours, prompting Lithuania to deploy officers to their shared border.
The EU said that it is monitoring 20 countries on Tuesday, including Russia, for their possible role in the transport of migrants towards Belarus.
They suspect Belarus of flying people from Middle Eastern countries and dumping them at EU borders, or facilitating their journeys, in order to destabilise the bloc in retaliation for Western sanctions.