There's a Days Hotel almost opposite (London Waterloo). I've never stayed there, but it certainly looks cheap
A 5-10 minute stroll away along the Cut (quirky vibe - also take a short detour along Lower Marsh) is the Travelodge, which I have used. It's exactly like every other Travelodge, which is a good thing and a bad thing simultaneously.
The area's actually a great place to stay, if you like walking. It's minutes away from Waterloo Bridge, which is the best view of London bar none - the Kinks were right. Once across the bridge, you're pretty much in Covent Garden.