Daisy Dee, I budget £100 per week for 3 adults and 1 child, and never spend that much so I am sure you can get it down.
This is what I do; (well, plan to do until I fall off the budgeteering wagon)
Write down 31 meals onto a spreadsheet (some can be repeated - example, sunday roast x 4). (If you get to a point where you are stuck, you can ask on here for ideas but someone on there put Risotto, which my lot would never eat and similarly I buy shop-made cornish pasties, which some on here would never entertain, so it's personal to your preferences). My meal plan is full of heavy carbs and stodge, but I have three blokes in the house and this is how they like to eat.
Then in the next columns write everything I need to buy to make those meals.
You could either do a 4 week menu plan, But I just use the 31 meals to chop and change to suit our circumstances (i.e. there's no point in making a meal from scratch if we're out all evening so need something quick that I can microwave)
So on my shopping list I write down all the stuff I need, but then go through the cupboards and cross anything off the list that I already have got in.
Then I write down breakfasts
write down stuff I need for packed lunches
write down stuff I need for laundry
stuff I need for cleaning
any toiletries
Definitely do a Tesco shop online if you can. Delivery is only about £3-4 and they are always sending e-mails and coupons for money off, or £5 off your next shop. You're then not tempted to chuck extra stuff into your trolley.
Do you have any discount stores where you can get items cheaper than supermarket? I don't buy cake bars / chocolate bars / treats / school pop in my main supermarket shop if I can help it, I go to Home Bargains. £20 can get you massive carrier bags of sugar-laden crap that then lasts all month (if you hide it). Or yes, baking your own treats would cost less, but I never have the time.
There's a frugal thread over on the credit crunch board which I am evangelically posting upon now...