We are on opposite sides of the Pond, so I'm no help in sourcing styrene on your side. Over here there is Evergreen Plastics and such. As to shaping styrene, You can mark straight cuts, then score the line 2-4 times with a sharp knife, then snap the pieces apart. Clean up any roughness with a bit of sandpaper.
As to gluing styrene:
Buy a can of MEK (Methyl Ethyl Ketone) from your hardware store (about $9 a quart in NW Washington). Get a small glass jar with a tight metal lid, such as pickled artichokes come in. Make 1/4" hole in the lid, of a size for which you have a tight fitting plug. Screw the lid on tight.
Pour in about ¼ cup of MEK. Cut up a teaspoon or 2 of styrene into chips and put in it the jar. Install the plug. Go have a cold one, or wait until tomorrow (gives the styrene a chance to dissolve). You now have enough cheap styrene glue to build the Queen Mary at 1:24. Apply with a small brush or a syringe or a dropper. This can be used to fill very small gaps in styrene, too.
My Loyal Volunteer is built this way. This technique is given in the kit's instructions, from Model Slipways.
Good luck.