How much cash can I carry when travelling to the US?

There is no limit, if it's more than 10'000 USD however, you need to declare it:

There is no limit on the amount of money that can be taken out of or brought into the United States. However, if a person or persons traveling together and filing a joint declaration (CBP Form 6059-B) have $10,000 or more in currency or negotiable monetary instruments, they must fill out a "Report of International Transportation of Currency and Monetary Instruments" FinCEN 105 (former CF 4790).

There is no limit to the amount of cash you can carry, however if you are carrying more than $10,000 USD (or equivalent in foreign currency) then you must declare it (full details on how to do that at the URL above).

However bringing cash is very rarely the best strategy for foreign exchange. Although your credit or ATM cards might charge you a fee when you use them in the US, they generally offer an exchange rate that is far better than you'll get when converting GBP cash to USD cash. The difference in exchange rate will normally at least cancel out the credit/debit card fees.

If you convert too much cash and have to convert it back to GBP when your trip is over then you lose out again as once again you'll get a poor exchange rate for the conversion.

Cash also leaves you at risk of losing it and/or having is stolen. Even if you have travel insurance it normally does not cover the loss of cash.

There are multiple questions on here regarding the best way to manage money when traveling - I suggest you do some searching and you'll find the better options than taking physical cash with you!

Entering the U.S. with over $10000 in cash (or equivalent in any combination of foreign currency) will require you to fill declare the cash and will raise a few red flags. They may require proof of where you earned the money and ask why you're choosing to bring it to the U.S.

Typically, withdrawing money from an ATM is an even better option for getting local currency than exchanging it at your bank. Simply use a U.S. ATM with your UK bank card to remove funds from your account in dollars. This will sometimes incur a fee from your bank, but it is possible that your bank will reimburse you for these fees. Check your bank's website for more details.

Since the U.S. Dollar and the Pound are both major world currencies, foreign exchange spreads should be very narrow. Be sure to compare rates. Generally, you will get the worst rates at the airport and the best rates by withdrawing at an ATM.

Consider also using your credit card. Some cards have an overseas transaction fee, but if yours doesn't, you can bring less cash by using your card for most purchases.