I have never been to London, and am also travelling solo.
I am taking the tube from the airport to the hostel, its only a 5-10minute walk up the road from the tube station. See the map below.
Follow the blue line until South Kensington, Jump onto the green line, get off at East Aldgate. Then just follow Whitechapel High Street. On the next intersection take a right into Leman Street. Just follow Leman Street for 5-10 minutes. Once youÂ´ve passed underneath a railway bridge youÂ´ll reach Dock Street. The wombatÂ´s City Hostel is located just next to the little Church on Dock Street number 7.
Heres a map of the tube lines =)