I've tried myself to report vulnerabilities[1] and it's nearly impossible to find even the most generic of contact emails. I usually end up passing the info on to friends who do more gov work than myself. There REALLY needs to be a generic cert/security@gov.uk email somewhere.
[1] not going out of my way to find anything, but in the past if i receive a (usually HMRC related) phishing email from a .gov domain, i'll try and dig up a CERT email, or JANET if it is university related.