Hi Fletcher and welcome to the forum :
In order to answer your question, it would help if I knew what you were hoping to make. You've said that you've bought a Chardonnay kit, is that on-the-go yet?
Where are you based, have you found a LHBS (Local HomeBrew Shop) or do you have a local branch of Wilkinson's?
First off, you need something to ferment in. Glass demijohns (or DJs) are best but around £6 each unless you can find any at charity shops, car boot sales or through Freecycle. 5 litre PETs (supermarket plastic mineral water bottles) are a cheap alternative for short-term wines. You will also need airlocks and drilled corks or bungs. You also need at least one spare DJ when it comes to racking.
Hygiene is all-important so you should have some cleaner/steriliser in powder or liquid form. I use powders like Steri-Cleen or Young's cleaner & steriliser for my DJs and any plastics, and a Milton type liquid steriliser or cheap thin bleach for my other glassware. You will also need a bottle brush and a DJ brush.
A hydrometer and trial jar is essential, £5.
If you're likely to be making wines from fruits you will need one or two large, lidded buckets, a long-handled plastic spoon and some method of straining such as muslin or nylon bags. Any decent LHBS should have 3 and 5 gallon buckets. If you're making large volume wines, the Young's 5 gallon fermenters (around £11 from Wilko) are excellent.
If you are making kit wines then everything should be included. To be honest I wouldn't really know, although I am quite a prolific winemaker I have never used a kit and never will. If you move on to juices or fruits/veggies you will need pills, potions and powders such as Campden Tablets, Pectolase, Citric Acid, Tannin, maybe Glycerine, and of course yeast and yeast nutrient. These are usually in the range of £1-2 per pot but go quite a long way.
Juice wines are dead simple and should give you something really quite acceptable for around 50p a bottle, and
this thread should show some basic guidelines.