you will need a reader's ticket to progress beyond the front door, and this did incur a small charge, but not sure if that applies still - if you bring their web site up on the screen you will see what they require from you prior to letting you loose in the main rooms for research.
Would be disappointing in the extreme to make the sort of journey you describe and find a problem when you reached Kew. Wish you luck if you do make a visit. Up to twelve items can be pre-ordered - by phone- a day or two in advance - this does save a wait of up to an hour or so, which happens if you wait until you arrive before ordering.
It's not difficult to run down the CLASS III Nos., plus the accompanying Registers which provide text data of company names etc. - if you have a question, and you think it possible I might be able to help, let me know some time.
If it's of any interest I have a surplus photo-copy set of the Blue Book pages which you are welcome to have gratis - a few of the pages have my annotations - very discreet and almost unnoticeable, and they don't in any way affect the data.
Just a thought - send me a PM with postal details if of interest.