Without knowing your budget it's more than a little difficult to say what would be good yet 'cheap' accommodation.
If you'd like to stay near King's Cross, have a look at some of the modest but decent bed and breakfast hotels: the Montana Excel, Meridiana, Crestfield, Jesmond Dene and Alhambra.
Just along the Euston Road from KX is the newly refurbished YHA St Pancras hostel, certainly worth a look, as is the YHA hostel on Bolsover Street.
The very pleasant Arran House Hotel on Gower Street offers budget accommodation, three or four bunk beds in a room on the lower ground floor. The hotel is very nice, though, and the buffet breakfast is substantial.
If you'd like to stay near Victoria, have a look at the small but decent Luna & Simone Hotel.