I used the Edge Health estimate which we've already discussed. They calculated 22% for England as at 3rd January. I then calculated the number of people who had been infected since 3rd January (100k x 16 days = 2.5%). There's the 25% starting position.You're double counting, and best estimates for infected are in the region 12-20%, not 25%
Even if we take your 25%, the correct maths is:
Vaccinated: 21 million
Not vaccinated (67-21) = 46 million, of which 25% = 11.5 million have had it.
Either vaccinated or previously infected: 21 + 11.5 = 32.5 million, 44%, very much a best case scenario.
You like Eds have forgotten that 7% have already been vaccinated.
25% + 7% plus 14 days @ 500k takes you over 50%.