OK, on the food front, I also have a 'special' diet (dairy free). Admittedly there's only one of me, but my weekly food shop rarely goes over £20, I don't see why you can't do it in £100 for a family of 5.
-If you're also dairy free, Alpro is regularly discounted in Sainsburys. When it's down to £1 per carton I bulk buy the UHT ones and keep them in a cupboard, particularly the almond and coconut ones you can't taste the difference once it's chilled.
- Buy meat when it's on offer, most supermarkets will do 3 for 2 every few weeks. Split into portions in tupperwares/food bags and put in the freezer. I often eat vegan but meatless Monday seems to be quite 'in' at the moment, curry with chickpeas or tofu is significantly cheaper than with meat, so you only have to swap one meal a month to make a small saving. For spaghetti bolognese/chilli con carne, buy packs of sausages instead of mince and pull the meat out of the skins, much cheaper and looks more or less the same.
- invest in some tupperwares and prepare your own lunches if you're out and about. It's amazing how much I save doing this, sometimes I will take a packed lunch into Starbucks if I'm meeting up with friends there and just buy a coffee but eat my own sandwiches/salad. They don't care. And if you are going to somewhere like Starbucks regularly, get a loyalty card.
- look at the kind of fruit and veg you're buying. Often supermarkets will charge you a significant amount extra for pre prepared/fancy packaging. Don't do it.
More generally, a diary is definitely a good idea, I have a spreadsheet on which I record every penny that comes out of my account and what it goes on. I then colour code according to essentials (food, prescriptions, train fares etc), clothes, entertainment, socialising etc. Easy to look at it and immediately see where the money is going that way.
Why the expensive day trips? Go on walks together, bike rides, take up Geocaching, do crafts together at home. Book train tickets online in advance if you're going on a daytrip, often you can get major discounts.
How about running outside and investing in some home weights and a yoga mat instead of the gym? I would love to go to more yoga and dance classes than I do but I can't afford it at the moment, so I do a lot of home yoga practice and one class a week, few dance classes and go on runs in the local park, which is working for me.
My hair also grows insanely fast but I can only afford to have it cut twice a year so when it is cut I cut about 4 inches off and let it grow back out. Is that not an option? £57 a month on hair is 
You don't need to put £250 a month away towards holidays. You really don't. Ditto £75 on gifts and £75 towards xmas.