"Can I just rock up to Kew to research a relative who was naturalised or would you advise me to book a reading room visit."
Yes, you can just turn up, but you will have to wait for them to locate any documents that you wish to consult.
I would very much recommend making an appointment as they will ensure that any documents you wish to see will be ready and waiting for you.
"I have never been to Kew before so I have no idea what to expect."
Coincidentally, another person asked about visiting Kew a few days ago and this was my reply to her:
Before actually visiting The National Archives (the NA) it's best to search online to see if they have the actual documents you're after.
Some records are available to download online. There is a charge of £3.50 to download these, but, if you register with the NA then they are free of charge.
Sometimes, records are not available to download. The only reason to actually visit the NA is if you want to see a document that is not available online.
Below is an image of the message you get when a document isn't available online. If you see this message then you have to go to Kew to see the document.
"I think you have to book a timeslot for Kew as well which will need some planning if not close."
No, you just need to book a particular day and you can turn up anytime on that day you like.
If you've never been to Kew before and you want to view any documents you first have to register for a Reader's Ticket online which you do when you book a visit:
https://www.nationalarchives.gov.uk/book-a-reading-room-visit/
So, you say what date you want to visit and then provide a list of what documents you want to see.
They also have desks with camera stands. So you just screw your camera to the stand facing down (or attach your phone) and then instead of having to take notes or anything you can quickly and easily take a photo of every page of the documents that you are looking at.
This makes things so much easier but you do need to specifically request a desk with a camera stand.
The NA can be a bit of a trek to get to. I come into London on the train into Kings Cross and from there take the tube to Kew Gardens. It's then about a 10 min walk to the NA.
When you arrive there is a cafe there but it is horribly overpriced and not very nice.
You then put all the stuff you're not allowed to take into a locker:
https://www.nationalarchives.gov.uk/about/visit-us/researching-here/can-take-reading-rooms/
and go upstairs. If you haven't been before then they will take your photo and print out your Reader's Ticket.
You then go into the reading room and head to the desk. They will typically have your documents waiting for you in a locker. You then go to that locker and take the document or documents and then go to the desk that you have been assigned.
You then take your photos or anything else that you want to do and then, when you're finished, you return the documents to a different desk.
But the thing is, unless you can find the documents you're looking for on the NA website then going there in person won't help you at all. You really do need to identify what documents you're interested in and for them not to be available to download.
"I have got some information from Kew but I thought I would get more, it is very very basic - his name, date of birth and place he came from and I think if I actually go over to Kew I might get to see more information."
Depending on when he was naturalised then other sources such as as the Ancestry website or the FindMyPast website (both of which require a payment) may be a better option.
Information up until 1939 is readily available. After that date there is really just births, marriages and deaths along with some electoral lists.
If you would like to send me a private message I can do a quick check on both of those websites (it'll just take 5 minutes or so) and can let you know if they have any information or not on the person you are looking for, to save you the expense of joining the websites if they don't have any further information on this person.