Hi Tristan,
I'm sure you will get a range of different opinions on this, so I will throw my hat in the ring first.
First of all I don't think you should look to create two separate sites. I'm assuming the current site lives on the .com. Any site migration to a .co.uk structure could put you rankings at risk and you will see some flux in organic traffic. Building a .com/us would also allow you to leverage any authority from the existing site to help new pages rank quickly.
So.... should you build a .com/us and a .com/uk
This really depends on what the business plan is going forward. If the site is going to continue to scale, particularly in the number of products, it may be worth taking this hit now and rather than further down the line. If the number of pages are limited and you don't see this as much of a problem, you may look to continue using the .com for the UK and generate a .com/us for the US audience.
I'm inclined to recommend just building out the product pages, however you should also consider how this would be incorporated within navigation. How would a user return to a US page for example if they visited a UK page?
Hopefully this give you a few answers and a few more points to consider moving forward.
Tim