I have seen adverts for making cotton model sails and I think people are looking for 200-300 quid for a set. Cotton sails will look better than any synthetic. You can use bed sheet, and then wash it to pre-shrink the cotton. You could also use more expensive Egyptian cotton from a model making supplier.
There is lots of stuff about making sails and how to choose the best direction/orientation for cutting (relates to the weft and weave, the direction of the threads) it sounds more complex than it is (NB only really important if you are going to make this a working model). I would then cut a paper template of finished sail area, and then take the whole lot to a local seamstress (or find someone with a sewing machine who want to earn a few bob, and ask them to do it. They will hem all of the edges and make it nice. As you are in London, there are fashion design students who will maybe have more time for a little job like this.
Any seems that would be in a real sail can be mimicked with a line of stitches, or even a pencil.
Once the sails are made you can sew a bolt rope around the sail yourself, it does not take long, or get your sewing person to do it for you. Again, lots of instruction on line for this. Loops in the bolt rope can be used for attaching your running rigging, you don't need to worry about using grommets and eyelets.
I made a set of sails myself, did the sewing and made a mess of it. Next time I will make the cutting patterns from paper, and ask someone else. The bolt ropes I did myself and they are OK.
If you are going to put her on the water, once the sails are made, you can buy water proofing fluid designed for cotton jackets, and that will stop the tendency to rot. This can be purchased in outdoor sports shops. I got mine in either Blacks or Millet's.