Alex, there are a lot of boots around which would fit your requirements.
Leather boots needn't be heavy, so I wouldn't automatically dismiss them on those grounds. Scarpa's all-leather Rangers are lighter than both of their fabric boots which John mentions above, for example. And leather can be waterproofed without the need for Goretex. A non-Goretex boot will always dry out more quickly than a Goretex-lined one, which is a consideration for multi-day travel. Also, a leather boot can be made with only one main piece, reducing the amount of seaming. Seams are usually the first area to wear, and to let in water. And whereas Goretex will eventually wear or tear irreparably, leather can be reproofed with brush-on wax ad infinitum.
Manufacturers are keen to push fabric because not only is the basic material cheaper, they don't need Italian craftsmen to put them together, so manufacturing costs are lower. But it doesn't mean fabric is inherently better overall, or more suited to everybody's needs.
That said, you will find a far wider range of fabric boots than lightweight leather to choose from. A good fit is by far the most important criterion for purchase and material is really secondary (for your purposes anyway). Very few of the major manufacturers' boots are total rubbish, and most have their fans.
By the way, London shops don't necessarily carry all the styles they show on their websites in all sizes. If you're hunting a particular boot, it's a good idea to phone first and check before you make a special trip.