I am single and 25 and am currently living off £13,000 before tax (although that's not in London). My take-home is about £230 a week and I am just about scraping by on that salary - paying rent, bills, food and running a car, although I am hoping to get a graduate job soon that will hopefully pay somewhere between £20,000 and £25,000
.
You shouldn't have to pay any US taxes on your salary, unless you are earning over about $85,000 a year (over £55,000), but you will still need to file US taxes each year when you are in the UK.
£28,000 is a very good salary for a single person to live off - it's about £3,000 above the UK average salary and many families survive on less annual income than that
. Your take-home salary should be about £400 a week after taxes and NI (you can also calculate it here:
http://www.thesalarycalculator.co.uk/salary.php).