Local Housing Allowance rules
Since April 2011 if the rent you pay is less than your standard Local Housing Allowance rate then your eligible rent is used to calculate your Housing Benefit or Housing Costs element of Universal Credit and you do not get to keep any amount of the difference between your rent and LHA rate.
Old Local Housing Allowance rules (pre-April 2011 claimants)
Before April 2011, if the rent you paid was less than your standard Local Housing Allowance rate you could keep up to £15 a week of the difference. This provided an incentive to find a cheaper rent.