Yes it can. If the Bank of England base rate goes down, so will your simple rate, which is is the total interest rate you pay on your card. 

Your personal rate is an interest rate we set just for you. It’s based on a number of things, including your credit score and credit history. We add this to the Bank of England base rate to get your ‘simple’ rate, which is the interest rate you pay on your card, before it compounds. For more information on Interest visit amex.co.uk/interest.

The Bank of England base rate affects how much we have to pay to borrow money. If the base rate goes up, so does the cost of borrowing money – for both lenders and customers. Similarly, if the base rate goes down, we can pass these savings on to you. 

If the base rate changes, the change will usually apply to your credit card from the day after your next statement date. 

• If the base rate goes up in the 60 days before you take out the card, we won’t apply the change until the day after your second statement date.
• If the base rate goes down, we’ll apply the change the day after your first statement date.

In both cases, we’ll include a message on  your statement to let you know about the change, what your new rates will be and when the new rates become effective

Yes we will. If your interest rate is changing because the base rate has changed, we’ll let you know about base rate changes on our website and in the press.
We’ll also tell you this in a message on your statement before the change happens.

If your interest rate is changing for any other reason, we’ll give you at least 60 days’ notice if it’s going up. If it’s going down, we’ll still give you notice but might make the change sooner.