I have done a bit of living without a fridge or large budget, so if it came to it, the main trick is to "overlap" meals so you use up the ingredients quickly, and then change to something else.
Stop thinkiing in terms of breakfast food. So get up in the morning, buy baguette(s), small pack of cold meat, tomatoes, bag of apples. Have a sandwich for breakfast with a coffee, and add porridge and an apple if you need more food. Tin of quick cook oats in the room and you can make your instant porridge cheaply.
Make sandwiches using the same cold meat, tomatoes, baguette for lunch. Flask of coffee from the hotel, couple more apples, crisps from a multipack.
Another day it's tuna, spring onion, bananas, wholemeal bread. The fruit lasts a couple of days anyway, and the bread too. So next day you're just buying chicken and cucumber.
Your food costs are coming in at about £4-£7 before the £20 on dinner, which is probably not much more than they would at home? You just use your protein and salad ingredients more intensively, plan ahead and pack the equipment, and vary your evening meal. Oats, mustard, peanut butter, dried fruit and nuts are good staples to have in the room. It's very doable. Not to say it should be necessary, but you can keep the costs down.