There are several different sizes of 26" rim. Here are the three you will come across if you don't start collecting really old bikes.
First, 26x1.5 (559). This is the size of mountain bike wheels, the 26" tyres you can buy in Tesco.
Then, 650a, 26 x 1 3/8" (590), which was used in the size of British bike wheels, very long distance old-fashioned world touring bikes (it was the one rim you could buy anywhere, once), and cycle speedway wheels. Becoming a bit of a rarity, but there are still lots around.
Finally, 650b, 26 x 1 1/2x 1 5/8" (584), which is what you have. It is starting to come back into fashion and there are a wide selection of rims available.
A tyre that says 650a will be too big and may jump off the rim. A tyre that says 26 x any decimal instead of a fraction will be too small. You need 650b.
There are plenty of 650b tyres here:
http://www.sjscycles.co.uk/tyres-26-275 ... pt348_pg1/
I would suggest the Schwalbe HS159. A good medium quality tyre, ideal for a bike you don't want to think about much. Michelin World Tours are not what they were in the past, it is worth spending a little more for fewer punctures.