He would not necessarily be in London . The prison service do not reveal which prison any individual prisoner is in. A prisoner that has committed several murders will be in maximum security prison category A .
He could be in any of the maximum security prisons in the UK location of any prisoner is confidential information.
As Jno indicates, it's probably unlikely that any London prison would be used.
HMP Belmarsh is the 'top security' prison, where many serious offenders are housed - but that's more to do with the perceived risk of escape (or of them unlawfully contacting people outside the prison for the purposes of carrying on illegal activities, or witness intimidation).
HMP Durham and HMP Highpoint (in Suffolk) would be far more likely to be used, but HMP Maidstone might be the most likely choice.
HMP Brixton doesn't have a suitable unit. Neither (to the best of my knowledge) does HMP Wandsworth.
You can see from the list that Belmarsh is the only high security prison in London so that has to be the most likedly if you are sure he is in London.
The only way to contact him is if you know his full name you can send a letter to him via ' HM Prison Service' they will pass the letter on to him , but he does not have to reply or say where he is. It is down to each prisoner to decide if he / she wants people to know where they are.
Thank you so much for your help, all of you!!! Until now I've used Belmarsh in my book, but now, after your answers, I'll change it to one of your suggestions. Doctordb, the book coming on just fine, thank you! A lot of hard work, but it's really fun!
Brixton was always the remand prison in London, though Pentonville was used on occasions. Ashford, near Heathrow Airport, was the remand centre for prisoners who were not adults. The government plans to make Ashford a normal prison. Nowadays, high security- risk prisoners (viz. terrorist suspects) are remanded in Belmarsh
Bit of further research is unable to find a specific remand prison for the Central Criminal Court, the Old Bailey, probably because it takes some serious cases such as murder from a wide area, not just inner London, and therefore the remand prisoner might be held outside London, pending his big day out. Brixton remains a safe bet. Apparently it doesn't take remand prisoners for Southwark Crown Court any more; they are held in Wandsworth; but that seems immaterial.
Just a thought but a child murderer would need to be protected from the other prisoners who would try to kill / injure him. So such a person would be sent to a prison that has a 'vulnerable prisoner unit' I am not sure Belmarsh has such a unit.
If you want a good idea of life in Belmarsh then read Jeffery Archers 'Prison Diary Vol 1, Hell' it is about his time in Belmarsh and is very descriptive and true. It also describes the punishment metered out by the other prisoners to someone who has commited crime against a child, scary stuff !