When the climate began to warm 20,000 years ago, the enormous British Ice Sheet was no longer stable. It rapidly thinned, retreated and melted away. Glaciers did not immediately dissapear over all of the mountains, but remained in parts of the highlands for thousands of years. An excellent article about one episode of more recent glacier growth is available here: http://www.antarcticglaciers.org/glacial-geology/british-irish-ice-sheet/younger-dryas-loch-lomond-stadial/the-loch-lomond-stadial/

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Some evidence suggests that small glaciers survived in the high corries of the Cairmgorm mountains (shown above - looking down on Loch Avon) as recently as a few hundrew years ago.