On 19 April, about 68% of adults had covid antibodies, similar to your figure, so I agree on that (source ONS)
However, on 19 April, 62.5% of adults had one dose of the vaccine, or if we allow 14 days to acquire the antibodies, then on the 5th of April, 59.8% had at least one dose of the vaccine (source gov.co.uk). Far higher than 31%.