Looking for a 1 bed flat or house in London

Hi, I live in a 1 bed flat in Bedford, which has a separate kitchen, bathroom, bedroom and living room. It's on a residential street,which is quiet, and is close to the shops and less than a mile to the train station and town centre. There are bustops close by, for easy transportation to the town centre if you don't want to walk. Also, the main hospital is less than 5mins away. I am looking to move to London to be closer to family and will consider a 1 bed flat or house, with similar facilities like my property. Please do get in contact if you have any questions.