That would be my planned day:
- English breakfast-brunch. There is a recent post about where to have the best english breakfast in london.
- Camdem town, don´t miss cyberdog, and other weird shops. Maybe have lunch there, many "world" food from which to choose.
- Regent park is not far, maybe take a bus to sightsee a little. Stay a while there
- Walk south till regent street, quite posh area... visit apple store, hamleys, virgin... Picadilly circus..
- Leicester Sq, Trafalgar Sq, maybe a litlle walk to covent garden and then back to trafalgar via the Strand, (Temple area for an extra walk), then down to the Big Ben... Of course, all the time you have the museums if you want to stop (I REALLY like national portrait gallery).
- Then enjoy the southbank till tower bridge, stop at pubs or restaurants The borough market area should be ok on sundays for a quick dinner.
This takes easily a full day
Other areas to show:
Camdem town channels
Brick lane and nearby for a multicultural view
Notting hill, then go south, then parks
You have londonwalks (i.e. jack the ripper and the like, and they have special ones also). You may want to research on audio tracks to download from internet (cheap or free) for walking routes.
There are some people offering cycle tours (i took a card from one lady at the soutbank once, but i lost it)
Enjoy London
Cheers