I'm not being silly. There's extra-thin double glazed units which are designed to replace just the glass in existing sash windows. Have a look at 'sashglass' for an example (not a recommendation, I've not used them). It's almost certain to be approved and will reduce noise and energy loss.
The weights operating your sash windows will need to be increased to account for the extra weight if you do this. Often they have to change the iron weights for lead.
Do you know if you are in an article 4 conservation area? If so, definitely check with your local authority before proceeding with any work. If you are not in an article 4 area, you should be okay as long as the windows are still in keeping with the area.
Below is a link to a guide we have created to help identify whether you need planning permission, although if there is any doubt about the need for planning we always recommend that you speak with your council directly.
mayfly182
OnePlan
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