British student loans are only tenable in the UK. There are limited options to use loans to finance a university education in the USA if you are a British citizen.
UK banks will be able to offer personal loans, but you will have to begin making payments during your studies and interest rates are considerably higher than a student loan.
If you are a US or dual US-UK citizen, you can apply for US federal student loans through the FAFSA website.
If you do not hold US citizenship, you might be able to take out a private loan if you have a creditworthy US citizen or permanent US resident who can co-sign the loan agreement with you.
Some US colleges will loan money directly to international students. You should contact each university’s financial aid office to find out the usual loan arrangements for international students if a loan is necessary for you to complete your studies.