First question, is it a listed building? This will greatly affect your options.
If it is listed, you will probably have to preserve the original appearance, which will mean no sealed double glazed units.
If it isn't listed, you will probbaly have to conform to part L1B of the Building Regulations (Conservation of Heat & Power - Existing Dwellings):
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Society for the Protection of Ancient Buildings maybe a good source of advice:
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pvc and wood will never have lower enough profiles not to be visually intrusive (you don't say how narrow the panes are beteween the mullions - if it's down to 50cm or less, the frames will have quite an impact).
You could get steel frames custom made (e.g. from Crittalls
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these will offer you the lowest profile of any frame. Nowadays steel windows have proper draft seals, can carry double glazed units and are available fully galvanised and powder coated from the factory - very low maintanence. These are especially good if you need opening lights with horizontal transoms - narrowest possible sightlines of any window (least visually intrusive).
Another alternative is to direct glaze into the stone mullions, using something like 6.4mm laminated glass. Glass is very cheap compared to windows, even the more specialist glass. It will look superb and just disappear into the stonework, downside is no openers of course. You'd probably want secondary glazing with that. If the windows are built into deep internal recesses that may be convenient, or it may be impractically difficult. The visual apperance of glass straight in stone is great though.
Finally if you go for DG sealed units, be aware that you can order the spacers between the panes to be other colours than the standrard silver colour - certainly black or white is available. They can also do a somewhat narrower band (less visually intrusive) than standard.
Standard DG units are now 4/16/4 (4mm glass, 16mm air gap, 4mm glass), so that's 24mm of depth plus sealing strips (1-3mm) plus the depth of the frame - given that has to be accomodated in the exisiting mullion, that may well tie your hands to a single glazed solution with secondary glazing from inside the room.