If I am in the UK, does it matter if my web server is physically located in the USA?

You can but...

Legal Issues:

Personal data shall not be transferred to a country or territory outside the European Economic Area unless that country or territory ensures an adequate level of protection for the rights and freedoms of data subjects in relation to the processing of personal data.

That is known as "Data Protection Principle"

The UK Commissioner will evaluate the data transfer following these recommendations:

  1. Transfer of data to a third country (European Countries).
  2. Adequate level of protection of the guest country.
  3. Adequate safeguards (of data of course)
  4. Other derogation (will evaluate the overall respect of the other principles).

The first point obviously apply only if the DATA is kept in the European territory.

En example are social networks that, for performance issues, they need to distribute their data centers worldwide. In this case the Commissioner will check that the minimum required by the UK legislation is met in the third country.

Performance issues

It's hard to say, you have to make some theoretical calculus...

I found this bandwidth calculator that can help you, then, when you will have the numbers, you can ask your new provider to let you try to upload/download some files from one of its server, so that you can evaluate.

If they won't let you do it, well, you can look for another provider, or you can try some of customer web server (their internet sites I mean) that are using the same host provider (portfolios is the key).

You have to use some tools to check the network performance, if you use Firefox, I advice you to use https://addons.mozilla.org/en-US/firefox/addon/firebug/... It's just perfect