Phone/ Data? 

'Three' is a mobile network you can use to get a proper phone number. You can either purchase a phone if you have a sim lock phone OR... use a pocket wifi and use Line/SNS. However you must have a # if you want to work.

Bank?

Santander Bank is a good option. It's inside Goldsmiths University. 

Bedding?

Argo's, Lewisham Shopping Centre, or buy it online. OR... if your willing to, IKEA.