I'm not a veggie, but I don't eat a lot of red meat. I eat mostly chicken, turkey, fish, quorn and meat free products.
Its really a case of label reading ( with regards to veggie products) as a lot of them are quite high in fat. I have things like the quorn Swedish meatballs, Morrison's meat free meatballs, some of the quorn sausages ( cant remember what ones of the top of my head lol), meat free burgers.
Best advice I can give, is read every label of everything you buy, (remember everything should be less than 5% fat, so 5g of Total Fat Content per 100g food product) and also keep a food diary, either here online, or a wee notebook that you keep beside you. It will really help you keep an eye on your fat intake, and also help you plan your meals.
Good luck
x