Both the US and the UK state pension (Social Security, National Insurance respectively) systems are skewed (although in different ways) to benefit the low paid. In addition, both systems have means-tested supplements for retirees in hardship (SSDi in the US; Pension Credit in the UK). The non-means tested benefits in the UK are listed here:http://www.newcastle.gov.uk/core.nsf/a/wr_thebenefits_nonmeans and the official Web site is here:
http://www.direct.gov.uk/en/pensionsandretirementplanning/statepension/dg_183759One can "game" the two systems: indeed it is possible to buy credits in the UK (Class 3 voluntary contributions) although the cost has risen substantially recently. For the very low paid, and for those on State benefit, NI pension credits are free, or nearly so.
US residents abroad should try to get at least ten years' (40 quarters) of Social Security credits before reaching age 65 to become eligible for Medicare. There are several ways to do that, one is to waive the exemption provided by the Social Security Totalization Agreement for at least the minimum earnings required to get such credits. Google: 'quarters of coverage' for current figures. But the actual pension received from the SSA for persons also receiving a foreign pension may be limited by the Windfall Elimination Provision
http://www.ssa.gov/retire2/wep.htm This reduces US a social security pension by part of the foreign one to compensate for the low-paid skewing.
Those who do not have enough years of credits (10 or 11 as the case may be) to get a pension from the US or the UK may have their credits "totalized" into the other scheme (and/or other European/Canadian/etc. schemes) for calculation of that pension. But one can't get credit for the same year through totalization (the double contribution is lost); and for that and other reasons it's better to qualify for separate pensions from the two (or more) countries if you can. As I said, some strategy and "gaming" can be undertaken through self-employment, voluntary payments, trivial work for a friend, and so on -- depending on the rules in the particular country.