THere is an interesting page o nthe
CTC Website explaining tyres and sized, which can be applied to wheels.
Most tyres are now marked according to the International Standards Organisation (ISO) in addition to more familiar markings. The ISO size comprises two numbers separated by a dash. The three-digit number after the dash is the most important. This is the bead diameter at which the tyre fits onto the rim. Check the bead diameter of the tyres on your bike. If you’re ever in desperate need of a tyre and can find one with the same bead diameter, it will probably fit even if every other thing about it is different.
That initial two-digit number is the tyre section and roughly indicates the tyre width. Its actual width is normally less, but varies according to how the tyre is designed and the width of rim to which it is fitted. But the height of the tyre usually corresponds quite closely to tyre section, so overall diameter approximately equals the bead diameter plus twice the section. That’s how the diameter and circumference (Circ. – equals distance rolled in one turn of the wheel) are calculated in the Tyre Size Table. These figures are useful for setting your cycle-computer and precisely calculating gears.
Half of the bead diameter (i.e. the bead radius) corresponds with the distance from the centre of the wheel to the centre of a brake block. By comparing this dimension you can see if the brakes will reach when a different size of rim is fitted to your bike. Switching from 630 to 622 for example, needs another 4mm of brake reach.
This is exactly the change in dimension you are looking for.
Depending upon finances the stages I would take in your situation would be...
Examine brakes and see if there is a 4 mm adjustment possible
Buy a pair of decent touring wheels at 700c (Edited - SPA cycles have been brilliant for my wheels)
Fit and enjoy the wide range of tyres at this size
Of course if the brakes cannot adjust etc then this may be even more expensive.
Otherwise go to s "specialist dealer" such as St John Street who
have a range of "630" tyres including the Continental Gatorskins and Pasela tyres in 32 mm diameter
Hope this helps.