I am considering booking one of the travelodges in Central London but they all say they have no left luggage facilities. My flight arrives at 5:30 am! and check in isn't till 3pm. Any ideas where I can safely leave my one bag (carry on 19" wheeled) for that time?

Almost any other hotel will look after luggage before or after your stay, but Travelodges are apparently different. The main stations and airports have left luggage offices run by a company which charges £8 per item.
www.left-baggage.co.uk

We left bags at Euston station in April 2009. The process was very easy and the left luggage office was easy enough to find, although tucked out of the way.

The website given by GeoffHamer has all the information.

Thank you

I'd find another Hotel. Travelodge is not anything special and are not located in the most convient locations IMHO

We faced the same dilemma last year. The Victoria Coach station has a secure place you can leave your luggage. It was 3.50 pounds. Do a google map search so that you will recognize the entrance. We became a bit disoriented after embarking from the early morning chaos that is Victoria Station and walked around a bit before finding it.

Here is the TFL website:

http://www.tfl.gov.uk/gettingaround/1216.aspx

St Pancras station also has left luggage. If you're flying into Heathrow and taking the Tube into London, it's directly on the Piccadilly line, though you'll have to walk a bit to get from the Tube area to the trains/left luggage area.