I spent several hours on the Internet yesterday tracking down various members of my great grandmother's generation on the census returns. I also manged to find great great grandfather on the 1911 census! He was living with a newly married daughter near Spalding and working as a jobbing gardener even though he was in his mid 60s. The State Pension was first paid in January 1909 and was the princely sum of 5 shillings a week (about £20 per week now) and you had to be over 70 to get it so he wouldn't have qualified at the date of the 1911 census. I've just found out it was means tested as well so if if you had other income of more than 12 shillings a week you wouldn't have got it.
Only 5% of the population was over 70 so at the time the Government weren't taking on a huge financial commitment. Apparently you would forfeit your right to it if you had been in prison in the previous 10 years, were habitually drunk, or had been unemployed even though there were jobs available. In 1928 it was expanded to include anyone over the age of 65.
The state pension was brought in because people were living longer than they were physically able to work and the workhouses and the outdoor relief under Poor Law provisions were overstretched. I think many elderly relatives were incorporated into families but if they had no families who could take them in then the state had to take over. Though 5 shillings a week was not enough to live on even then. How has life changed!