No, you pay a percentage on your turnover.
For a cafe the percentage is currently 11%, but there is a discount of 1% for the first year of registration.
So if your sales in the first year (including VAT) are £100,000, you would pay the VAT man £10,000 - it doesn't matter how much VAT there is on your purchases (although if you buy any capital items, like funrniture, you can claim the input VAT for these).
Now if we assume that 90% of your sales are standard rated (it is probably more than that, so this is conservative) you would have output tax of 90% x £100,000 x 17.5% = £15,750. Now because most of what you are buying is food, your may only be paying input VAT on, say £20,000 of inputs (this is probably a bit high, which again is conservative) - so £3,500 of input VAT. That means that using the 'proper' method you will pay £15,750 - £3,500 = £12,250 to the VAT man.
So using these figures, you would be nearly £2,250 better off using the flat rate scheme - and because I have used conservative figures, it is probably more than that. And the administration is much easier.
You need to have turnover below £150,000 to use the flat rate scheme.