There is no standard basin size but the most common in UK bathrooms is probably approx. 550 x 400mm. Some luxury basins are considerably bigger than this while most cloakroom and en-suite basins are smaller.
It is usually (but not always) cheaper to buy a wash basin as part of a bathroom suite or as a set which usually comprises a basin, pedestal, toilet and cistern.
If you have a bathroom, ensuite and cloakroom and you are want to incorporate the same style of bathroom in each room, it is possible to have several different sizes of the same wash basin - Roca is one such manufacturer that offers this option on many of its ranges. One of the advantages of the current trend towards clean geometric shaped bathroom components is that a lot of them look very similar, so even if the bathroom manufacturer you have chosen does not supply the basin you require in varying sizes, there are bound to be several other makes that could match-in with the look of your other components.
If you do buy your basin separately from the rest of your bathroom suite then it is best to buy the basin and pedestal as the basin from one manufacturer will not always fit the pedestal from another.