This is a new one on me. I thought you qualified for the full state pension, if you were born after 1951 (men), after contributing National Insurance for 35 years. I've retired with 42 years under my belt. I've never heard anything to the contrary up until you've just posted that. Had you been paying into the system non stop up to your retirement or did you have breaks through your working life?
I retired at 60 - nearly 12 years ago - and had to pay for an extra few years of NI that was owing due to me being opted out by my employer. It cost about £800 for each year I owed, but the increase in my pension paid that back in less than 3 years.
Worth checking on the Gov.UK site.
A lot of folk think that once you reach the required age you automatically get the full pension. It's not so and catches a lot out.