When Mrs Analyst was recently expecting Junior Analyst, the question did come up very briefly. Notwithstanding the fact that - as stated in the OP link - the circumcision rate in the UK is 15%, and non-religious rate only 6%*, both our fathers were circumcised. My father actively chose it, according to my mother as a scam for bed-rest while doing his National Service (or she may just have got that from The Virgin Soldiers), while my father-in-law did not, it being down to a neurotic fixation of his mother's. Luckily my father did not visit it on any of his sons, and neither Mrs Analyst nor myself had any inclination to take the practice up again. As it was, Junior Analyst turned out to be Miss Analyst, so the question was even more moot.
* It may be worth noting that in the UK, many people did not recognise the sub-title of the South Park movie as a double-entendre, and merely assumed it was a statemnent of fact that the film would have a longer running time, would be on a larger scale, and have more profanity than the TV series.