The various student loan repayment plans (US student loans) will base payments on your adjusted gross income. It's a lot easier to file a 1040EZ (if you can) than have to provide all the documentation to the loan servicer every year, IMO. When it's time to do the annual recertification of income, you can select the option that allows the loan servicer to access your IRS return information.
Read the options and requirements carefully for the repayment plan you select. You can switch them at any time, but some are more generous for low income people than others. There are some that, if you pay on them for 20 or 25 years - depending on if you have only undergrad or grad loans - they will be wiped clean at the end of that time. Of course, then you'll owe taxes on the forgiven amount.... so yes, read all your options carefully and make sure you understand what each one entails before you sign up.
Note that if you had any income in the UK that wasn't taxable in the USA your AGI would not reflect those funds. Some of the income-contingent repayment plans have qualifying payments of ~0~ per month, based on your AGI being low enough. My own were slashed by two-thirds, because my social security was not taxable in the USA.
Good luck.