Oh dear, no wonder I'd had fuck all for years.
As you increase your holding from £1,000 to £5,000 or £10,000, the math shifts from "almost certainly winning nothing" to making a monthly or yearly prize highly predictable.
With the current [NS&I Premium Bonds] odds sitting at 1 in 21,000 per individual bond, here is how your odds of winning at least one prize scale across a single month and a full year:
Holding Amount Odds of Winning at least one Prize in a Given Month Most Likely Outturn Over 1 Full Year (Average Luck)
£1,000 1 in 21 £0 (High chance of no wins at all)
£5,000 1 in 4.2 £125 to £175 (Roughly 5 to 7 wins of the minimum £25 prize)
£10,000 1 in 2.1 £300 to £350 (Roughly 12 to 14 wins of the minimum £25 prize)