i have already answered this question ..but ..you do not have a floor to strengthen ..what you have is ceiling joist ..these are less than half the depth of a floor joist ...you are not allowed to add on top you must either run new joist alongside ..this causes serious problems ..you have to open up the roof both sides ..alter all the electric cables and pipework in loft ..or you add steels ..these fit from gable end to gable end ..in most cases ..and fit over the top of ceiling joist ..not resting on them ..the new floor joist then sit in the web of the RSJ..the only problem with this method ..or any loft conversion is height ....your first action is to measure from the underside of ridge to top of ceiling joist ..ideally you need 9 feet ..anything under 8ft is not worth doing for the space you are gonna create ..by the time you have added the new floor you have lost 9"..225mm ..unless you go the first route ..joist along side ..your next problem is insulation ..most rafters in roof are only 3x2 ..or 4x2 ..you need to add 100mm 4" of celotex inbetween rafters ..and still leave an air gap 1" 25mm ..so you will need to thicken the rafters ..then you will need to add thermal boards to underside of rafters ..normally 50mm 2" thick ..you will need collar ties under ridge ..again boarded underside ..all this reduces the size of room ..but must be done to comply with building regs ...this gives you some idea where the money goes on loft conversions ...however all this info if you are only ever going to use it for storage only ..even in future will be irrelevent ..but i will tell you this ...they are very hot on any alterations that have been done that has not been done under building control ..and if you try to sell in future and the works has not been passed you may struggle ..do it right ..do it once

Basically want to do my loft conversion but in stages; for now I want to strengthen the floor, put flooring boards and Velux windows (it will be only used for storage). How much would that cost and who would you guys recommend in London ?