Yes and No
In many ways I agree that in theory there is no difference, its just an address and the internet is a global domain for everyone and .com is a prime example. .com is always the first domain you try when you are feeling brave and can't be bothered to try a search engine.
However on the other hand, I find it very annoying when I search for a UK based company with a .com address. Why? Well because its a UK based company, regardless or not if it has branches in other countries. Online shops are the worst example, I want to know its .co.uk so it will be in pounds and I can be more sure the company is based in the UK, with a UK address.
My advice, keep the .co.uk its who you are.