I am flying into Heathrow on April 8th with my bike but will not begin touring until May 12th. I thought about shipping it from the states, but the costs would be way too high. I'm kinda stuck on what to do with my bike for those 33 days. Any suggestions?

There's left luggage at HR but I'm not sure how expensive that is.

There are multiple self storage units in and around London too but I'm not sure how they work since the fertilizer bomb plot.
directory services (yellow pages and thomson local)
http://www.yell.com/ucs/HomePageAction.do
http://www.thomsonlocal.com/

The major cycling groups in London who might help are
cyclists' touring club - http://www.ctc.org.uk/
London cycling campaign - http://www.lcc.org.uk/

Try calling/e-mailing around the bike shops in London and quiz them
These are some of the reputable shops

http://www.condorcycles.com/store.html - quite possibly the best in London

http://www.brixtoncycles.co.uk/find_us.html

http://www.bikefix.co.uk/index.php?unique=756a37c49fead929d121721d250b038d&get_ol_id=1&get_gl_id=61&get_sgl_id=&get_bsm_id=28&bsm_code=#a61

http://www.onyourbike.net/

http://www.sigmasport.co.uk/app/web/BlackMenu.aspx?qsMenuID=14&qssubmenuid=0

The bigger chains that may also help but I strongly recommend you avoid Evans Cycles.

(I briefly thought about offering my shed, but thought better of it. Sorry!)

The stores I know around heathrow ... you might try action bikes http://www.actionbikes.co.uk/acatalog/stores.html

The staines store is very close to heathrow, and the sheen store would be a reasonable place to get a cab to stop if you were travelling outside peak.

If you want to get your bicycle into central london outside peak hours, you could also use the tube. You can catch a train from heathrow as far as hammersmith, then change to the district line to wherever is handy for your destination.

http://www.tfl.gov.uk/roadusers/cycling/974.aspx

If you want to leave it at heathrow, left luggage is handled by these guys
http://www.excess-baggage.com/airport_terminal_services.php

cool, thanks for all the links!