Moving Drupal to a new host but same domain I am planning to switch web hosting provider for  one based in the UK, as the data centers and offices for my current web hosts are in the US which makes it a lengthy process if I need to contact them etc. I am going to transfer my domain name (so I think that all of my URLs will be the same) and I have downloaded my public_html directory and MySQL database to my computer. If I just upload everything to my new host will everything work?

I have checked and I know that my new hosts have similar spec'd servers with PHP 5, but it just seems a little too simple. The biggest thing I am concerned about is the different timezones and the MySQL database really. If it makes any difference, I will be using shared hosting.
Few things to check.

Which version of PHP? I've seen Drupal sites break going from 5.3 to 5.4

You might want to check what the TTL of your domain is. If it's long you'll have people visiting the new site and the old one at the same time. You can set it to 5 minutes (300) which should make sure everbody moves across to the new site at roughly the same time.

Stress testing. Can the new hosting actually handle the expected load? Things like uploading images will take a lot of memory.