What proportion of adults in Britain can ride a bike?
This may be the closest you're going to get.  It's not an exact match:

It's England not Britain
It's not how many can ride a bike, but how many do

Sport England's Active Lives survey says that 6 million adults in England cycled for leisure/sport and 3 million for travel at least twice in 28 days, over the year to November 2019.  Extrapolating from demographic data for England, there were about 43.6 millions adults in England in 2019, which means something like just 14--20% of English adults ride at least twice a month (13.6% assumes that all the &quot;travel&quot; riders also ride for fun, while 20.6% assumes that people only ride for one or the other, never both.  The latter is clearly unrealistic, so I'd assume closer to the lower figure.
This is in decent agreement with 2018 figures saying 11% rode at least once pre week (8% leisure, 6% travel). These 2018 figures are at leats partly based on an earlier version of the Active Lives study.
I think it would be reasonably accurate to assume the same proportions across the UK as in England.

Trying to figure out how many can ride is harder, but I'll have a go.  There are hints from recent data suggesting many people got back on their bikes in lockdown.  Figures from Scotland show that in some places recorded trips doubled, however that could just be the same riders going out more.  Cycling Industry News reports comparable figures.
A survey for HSBC/British Cycling (reported in BikeBiz) says that 19% of UK commuters are more likely to cycle to work post lockdown.  That strongly implies that at least 19% of commuters are capable of cycling.
Of course, when you consider whether someone can ride, you have to think about whether they can wobble along a deserted path, nip through traffic, or somewhere in between.  Crucially the context in which you ask someone will affect their answer - I'd expect a larger proportion of people to say they could ride if prompted by pictures of a nice peaceful path, compared to a rush-hour city.
Realistically, based on what I've quoted above and in the absence of hard figures, I'd estimate that a bit over 20% are capable of riding for practical purposes, while far more can handle a bike in ideal circumstances.