If you can't afford to pay in full, don't pay a penny.
The reason for this is that the statute of limitations in which they can sue you for the debt starts on the day you default (stop making payments) on the debt. By resuming your payments, you reset the clock, and at any time they can then sue you for the remainder under the original contract regardless of any new agreement you might reach. It's a really common dirty practice for collection agencies to say "sure, send us whatever you can afford" and then file suit the day after the check clears, since sending them money can be seen by the court as admitting that the debt is yours and valid.
Instead, if you've gotten away with it this long, and the original creditor has sold the debt off to a junk debt buyer, then you're probably okay.
Check out forums like creditboards.com or myfico.com for more information.
Once a delinquent debt is on your credit report, paying it won't help your credit score and in most cases will actually hurt it. For a negative item, age is the primary factor, and once it's negative it will always be negative until it disappears completely seven years from the first delinquency.
They can indeed sue you and obtain a judgment without your knowledge, so it might be worth keeping an eye on the civil court websites of the counties you've lived in to see if your name pops up in their online case searches (most have that).
Otherwise, unless you want to actively take steps to clear the debt from your record (and/or you feel a moral obligation to pay it) you don't have to worry about just leaving it be and letting time heal the wounds.
(edited to add since the question will come up: No, your US credit report does not follow you to the UK. The credit systems are completely different. Also, it's virtually unheard of for a collection agency to pursue you across international borders or sometimes even state lines for a debt as small as a $2000 credit card bill. The cost would exceed the potential return.)