How much budget do you need for renting an apartment in London? 🤔

I wanna rent an apartment within walking distance. Budget is 200-300 per week. Checked the official website, indeed, the closer to the school, the pricier it gets, haha. Still holding onto a glimmer of hope, hoping to stumble upon a steal, renting an apartment that's both close and cheap, haha, 🤫🤫. Hey folks, anyone got any high-value apartments to recommend? Preferably close to UCL! (Really not too familiar with London...)