This page lists some options for sleeping overnight, in case you have far to travel.
Travelodge: London City Road: £90, Farringdon: £60
Premier Inn: 1 Silicon Way, Old Street: from £59
Old Friend, Bethnal Green: £60
City Inn Express: £45+
The Luxury Inn, Dalston: £65
Kandara Guesthouse: £53-75
Commongate (5 miles; bus/taxi required): £45
Arlington Avenue guest house: £40 (so they claim; looks like it should cost more)
Check AirBnB - £25ish
Lots near Kings Cross (Northern Line from Old St/214/205 bus):
And a huge number of small B&Bs south of Euston Road.
There's also a 24-hours Starbucks and Costa in the station if you're waiting for a train.
Posher ones around london: