I found a 22 tooth sturmey Archer sprocket in my toolbox and decided it to put it on my Batavus, just to see what difference it made to the gearing. These bikes actually have Sachs/SRAM 3-speed hubs but the sprockets are interchangeable.
I'm not surprised they're usually fitted with puncture-proof tyres, in order to get the rear wheel off you also have to undo the hub brake securing arm, two chain tugs and remove part of the chaincase. You're then faced with what is effectively an oil bath. These bikes might be designed to be ridden in your best clothes but you wouldn't want to change a rear tyre wearing them.
I got the replacement sprocket on OK but the wheel then fouled on the mudguard, as the chain now needed lenghtening. I'd had a misadventure with my ASDA chain-tool the previous week so I decided not to risk it and put the original sprocket back on.
On the plus side I found that my Batavus actually has a 19 tooth rear sprocket rathter than an 18 tooth one, so it wasn't as high-geared as I thought, There was hardly any wear on the sprocket so the bike seems to have spent most of its previous life in a shed and should be around for some time yet.