Wordpress site address

[climo]

I've not touched Wordpress for 5 years and I'm no techie. However a small local charity with zero money has asked me to redesign their existing awful site. Like a fool I said yes.
This is a real basic question so bear with me. They have webspace and want to keep the old existing site until the new one is launched so I was going to build the new site within that webspace but in a new folder. eg
www.abcd.co.uk/newsite
and when ready take all the files out of the newsite folder into the abcd.co.uk root folder and put the old files in another folder.
Question is: Will this work? Will all internal links work? Do I rename anything?

I'll fumble around when I'm in wordpress and eventually my limited knowledge will come back, I hope.

[Diver300]

Yes, that will work.
If you have www.abcd.co.uk/newsite, and within that you have something.html, and it has a link to soemthingelse.html, you just need to make sure that the link is
<a href=somethingelse.html>text user sees as link</a>
and not 
<a href=http://www.abcd.co.uk/newsite/somethingelse.html>text user sees as link</a> which will work until you move it.

If you want to go to a subdirectory, then that is addressed
<a href=subdir/thing.html>text user sees as link</a>
and not 
<a href=http://www.abcd.co.uk/newsite/subdir/thing.html>text user sees as link</a> which will work until you move it.

If subdir/thing.html needs to have any links back to the root directory of the new site, they should be
<a href=../something.html>text user sees as link</a>
and not 
<a href=http://www.abcd.co.uk/newsite/something.html>text user sees as link</a> which will work until you move it.

It would probably be a good idea to search all the files for instances of "newsite" as there shouldn't be any.

[Pickled Onion]

While that's very good advice for a hand-crafted site, climo is asking about Wordpress. There's a good post here which gives several different methods.

[climo]

Thank you Diver300 & Pickled Onion. The linked article is the way to go.