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Well they're hardly going to stop air flowing, it's draught reduction I'm going for.
I've got gaps I can presently fit my fingers into around the sash windows. Well-fitted shutters with fairly wide slats are going to reduce the overall space for draughts, and whilst I think some air will bleed through the space around the slats I also think it's going to take the existing draughts and soften them up and spread them out so they're not felt.
Right now one gap in particular lands right on where a chair is :D
Velocio-
https://www.wickes.co.uk/Wickes-Extra-Thick-Draught-Seal-White---3-5m/p/161201 for gaps, or https://www.wickes.co.uk/Wickes-Pile-Tape-Draught-Seal-White---5m/p/161211 for small gaps, plus https://www.wickes.co.uk/Wickes-Seasonal-Secondary-Glazing-Film---6m2/p/210014 for the glazing will do more to keep the heat in than £5k of slatted shutters...
hoefla
How do slatted shutters reduce draughts?