So you've got £150/week for food and utilities. It's possible - people do it on £65 - but it is a lot of planning and brain work. Life is a bit of a military campaign. I bet you will get a big boost through tax credits though actually anyway.
I do a weekly £40 shop at Ocado and do the delivery pass deal (£9.99/mo but you can get offers to reduce to £5 sometimes) charge so it costs out at £2.50 for delivery and I normally save about £10 on offers. I find Ocado good value and the best quality foodwise, but I still top up at Lidl for things like dishwasher tablets and binbags and the Asian grocers for rice and veg. I bike it so I don't do big shops and I've found my inherent laziness keeps the costs down. There are cheap meal plans on here all over - £25 a week for families etc. I spend on average £50 including delivery and extras and special meals. Make sure you buy a meal for your cupboard whenever you have a pound or so leftover and then you'll always have something in off-plan.
I switched from Tesco because it worked out cheaper in the end because Ocado rarely substitute and when they do, it's sane. Tesco used to cost me money because I'd have to go back out to buy, you know, loo roll or whatever after Tesco had substituted it with a family pork pie and two balloons. If you buy your food shopping on a John Lewis card you can spend the resulting vouchers on shopping. Should be able to get at least 3 weeks of food free.
If you have to buy anything, buy it through Quidco. If you can, switch your utilities: moneysavingexpert currently has plusnet at £8.57/mo as the cheapest deal. Make sure you switch through a switching site that gives you cashback. I spend approx £22 a week on gas and electric combined and I am in all day. Also worth checking your council tax band. All clothes except knickers from ebay, of course, and if you put your partnership card on the Paypal account, you'll get points on them, too.
You can get a special deal from BT where you buy a year's line rental in one go, saving about £50. You can use Skype to call out mostly, will cut your costs. I don't have a mobile, that saves money.
Line your curtains, fill any cracks or gaps, wear a hat indoors, put a blanket on the bed, put foil behind the radiators, and apply for an insulation grant. Get a sheila maid and sell your tumble dryer if you have one. Stop buying kitchen roll and other disposables - use washable cloths. Make your own washing powder... It all adds up. I review our budget once a month and find a saving, even a small one, every month.
The lower I get running costs (invisible spending), the more disposable income we have and the richer we feel - it's better for the psyche.