Current UK pension is 221.20 GBP (11,502 pa).
If you delay your claim by 5 months, until the annual adjustment is made, you will have lost approximately 4,800 GBP that you could have been receiving.
If the pension increase next year is, for example, 10 GBP per week you will gain 520 GBP each year until you pass. So you will break even and start to profit after about 9 years.
If the increase is 20 GBP per week, break even will be around 4.5 years.
I hope my maths is correct.