A simple Google search will give you answers to this question.

I am not an accountant or a banker and this is not "professional advice."

From the articles you will see, it is clear that setting up an account for a foreign company is possible. However, you must provide plenty of paperwork to satisfy the bank that you are who you say you are.

Apparently there are online banks that may allow you to set up the account remotely.

Another caution the articles will show you is that while some bankers may earnestly give you the advice to set up a US corporation--which is indeed easy and inexpensive--if you do, you are then getting into the mess of having to pay US taxes.

If I could find out this information from good sources in a few minutes, you could have as well.

Simple answer is YES. The least complicated is to use a US branch of a UK bank such as HSBC or Barclays that you already have an account at. I did this when I ran a company in London that was selling into the US market. The US account was set up by the London branch office.
If that is not possible, opening a US account can be done, but you will need a US represenative, preferably an accountant, to go to a branch office with the required paperwork. You will be requied to obtain an EIN number from the IRS and will need to setup a US corporation and US address. Again this is rather simple to do and there are many online companies that can do this for you. There are a few online banks that can set up accounts for foreign corporations in a few days time, but prior to that you will need an EIN along with a copy of managing directors passport, plus one additional form of ID such as a drivers license, as well a UK corporate papers and US articles of incorporation.
Keep in mind that selling in the US means you will enter the US tax system and will need to file annual US and State tax returns so you will need good tax advice on which state to incorporate in. Hope this helps...
Cheers