The general's remarks come after the UK defence ministry said last year that it would cut overall numbers in the UK's professional army from 82,000 to 73,000 by 2025.
"Taking preparatory steps to enable placing our societies on a war footing when needed are now not merely desirable but essential," Sanders said in a speech at an armoured vehicles conference in southwest London.
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"Within the next three years, it must be credible to talk of a British Army of 120,000, folding in our reserve and strategic reserve."
Sanders, who steps down later this year, said the UK could not rely on its navy and air power, arguing that "we must be able to credibly fight and win wars on land".
UK allies were already doing so, he said.
"Our friends in eastern and northern Europe, who feel the proximity of the Russian threat more acutely, are already acting prudently, laying the foundations for national mobilisation," he added.
"Ukraine brutally illustrates that regular armies start wars; citizen armies win them."
Last week the chair of NATO's military committee, Admiral Rob Bauer, said civilians in member states should be prepared for a potential future war with Russia.
A large number of civilians would have to be called up if conflict accelerates in Europe, he added.
Earlier this month UK Defence Secretary Grant Shapps said that the UK wants to increase defence spending from 2.1 percent of GDP to 2.5 percent in the future.
Video Shows Ukrainian Troops Training in UK, General Staff Posts on Social Media
In a speech last week the minister said that the world was "moving from a post-war to pre-war world".
The UK, he said, must ensure its "entire defence ecosystem is ready" to defend its homeland.
Richard Dannatt, who was chief of the general staff from 2006 to 2009, compared the current situation to the 1930s when the "woeful" state of the UK's armed forces failed to deter Nazi aggression.
"There is a serious danger of history repeating itself," he wrote in The Times newspaper last week, calling for UK defence spending to reach 3.0 percent of GDP.
"If our armed forces are not strong enough to deter future aggression from Moscow or Beijing, it will not be a small war to contend with but a major one."
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