glad you're trying to make the change to veganism!! my best advice would be buy tinned food because it is so cheap (provided you buy the supermarket basic range version but it's still good quality). so tinned tomatoes, lentils, kidney beans, chickpeas, etc - they can really pad out a meal. also, focus on carbs. carbs will keep you full! so pasta, potatoes, rice, oats, cous cous - all super cheap.
it starts to get a little more expensive when you look for substitute foods. it's a shame that there isn't an cheap vegan cheese in the uk, but i guess it's because demand is lower so they can't afford to sell at a lower price. my favourite vegan cheese substitute is violife, which you can buy in supermarkets as well as holland + barrett + other local health food shops. it's around £2 a pack, but you can make it last, + besides, you're saving money on the rest of the diet by not eating meat + other expensive non-vegan foods. you can get violife as a spread (fab on crunchy bread), as a block (good for grating), or in slices (good for melting into things).
in terms of meat substitutes, other than beans + pulses etc, linda mccartney is the best. not too expensive - the brand does vegan sausages, mince, sausage rolls, pies. you can find regular soy mince quite cheap from supermarket own brands now + holland+barrett often has some good cheap meat substitutes in the freezer section.