EVA cannot recommend any particular accommodation but here are some possibilities. Transport in London is very expensive so if you are on a tight budget accommodation within walking distance is advisable. We have no information on cost, quality or availability - please contact the establishment.
Hotels nearby
http://www.strandpalacehotel.co.uk
Travelodge is cheaper - there is one in Covent Garden and cheaper ones further away around central London. See http://www.travelodge.co.uk/
Hostels - inexpensive ones nearby are:
LSE hostel, High Holborn
http://www.hostelworld.com/hosteldetails.php/LSE-High-Holborn/London/533
Pickwick Place, Bedford Sq
http://www.hostelworld.com/hosteldetails.php/Pickwick-Hall/London/7502
Astor Museum Inn, 27 Montague Street,
Bloomsbury, WC1B 5BH, London
http://www.hostelworld.com/hosteldetails.php/Astor-Museum-Inn/London/520
There are numerous search sites for both hotels and hostels - consult a map while you search.