The Russian military are continuing to withdraw from South Ossetia
The UK says it "would be a mistake" if Russia and Nato did not maintain links in the wake of the Georgian crisis.
Russia announced last week it was stopping military co-operation with the alliance, but stopped short of suspending full co-operation.
A UK Foreign Office spokesman said: "We believe that it would be a mistake to suspend all Nato-Russian contacts at a time when they are so much needed."
Russia fought a brief war after Georgia tried to retake South Ossetia by force.
Most of Russia's ground forces pulled out of Georgia last Friday, following a French-brokered ceasefire agreement between Moscow and Tbilisi.
But some Russian troops continue to operate near the Black Sea port of Poti, south of Abkhazia, and have established checkpoints around South Ossetia.
The Foreign Office spokesman said: "Nato-Russian relations will need to take fully into account the implications of the military action in Georgia."
Last week Russian Foreign Minister Sergei Lavrov said Russia was not going to "shut any doors" to future co-operation with Nato.
But he warned that the alliance had to decide what was more important to it - supporting Georgian President Mikhail Saakashvili or developing a partnership with Russia.
The Nato-Russia Council was set up after an agreement in 2002
At the time, Nato spokeswoman Carmen Romero responded by saying the alliance "takes note" of Russia's decision to halt co-operation but had no further reaction.
Nato had already said there would be no "business as usual" with Moscow unless its troops pulled out of Georgia.
However, it had stopped short of freezing co-operation with Moscow.
Under the 2002 agreement that set up the Nato-Russia Council, the former adversaries began several co-operation projects.
These included allowing Nato to transport by land through Russia non-military supplies for the bloc's operation in Afghanistan, developing battlefield anti-missile technology, joint military exercises and help with rescue at sea.