Residents of Kipling Estate received a letter sometime last year letting people know there were garages available to rent. I know they still had some around xmas. I should think they still have. You would need to contact the estate office (don't know which one but I think it might be the one on Leathermarket St.) There is supposed to be a Southwark Council waiting list but obviously it doesn't work. I'm supposed to be on it and I've never been offered a Kipling Estate garage. The council website says you will need to show a car or motorbike license but if they're sitting empty they might let you have one anyway.
It's not quite SE1, but just across the river near St Katherine's Docks I aware of a few privately owned and managed lock-ups and garages.
As part of the Enfranchisement process, the owners of Burr Close, St Anthony's Close and St Katherines Way developments were given the option to buy garages and lock-ups on the estate. Many people took up the opportunity and I believe these units will now potentially be on the market to rent.
A search on Google or web sites like ParkAtMyHouse.com should throw up a few options.
There are a dozen unused bicycle sheds on the forecourt of Northfleet House advertised on the notice board as being for rent at £12 a year. Too small for a trailer I imagine but certainly hold a few bikes.
The pram sheds are meant to be for Tabard residents. There are loads of Tabard people who have been on a "waiting list" (which I suspect does not actually exist, or at any rate has been forgotten or lost or both)for years.
Thanks Nihil. St Katherine' a bit too far but will check out website. Will check out Northfleet also, thanks Phoney. I am ex-Tabard resident Ms.Jo and I was looking for a shed etc. when there also. Maybe they will rent me for time served.
mikeq, I have a lock up in SE17. It's got hardly anything in it, so if you want to store things there you're welcome if you'll help with the rental. PM me if you're interested and I'll give you the details.