OP, at the risk of sounding like a blunt arse and be slightly dismissive of some more speculative but well-meant replies (still waking up from 4hrs crap sleep after a night shift) I’ve pointed you towards relevant legislation and I have experience in using it. Your employer is a business (which includes public authorities). The legislation refers to users (of the equipment), not to employees, so the fact its a home is a red herring. The computer equipment belongs to you, the home, not to the users.
I spent 2 years on the Professional Standards Dept within Thames Valley Police, investigating other coppers. The evidence we gathered has been tried and tested in court
http://www.sloughexpress.co.uk/News/All-Areas/Slough/Suspended-sentence-for-cocaine-fuelled-police-officers-having-affair-15022.htm
Today, the court heard that police became suspicious during a purge on the personal use of force communications equipment,
In other words, if you send an email at work (in a police station!) about buying cocaine, you are a bloody idiot.
What you are being asked to do is lawful, but whoever owns the home should know what rules govern the activity and have a policy in place to ensure it is practiced lawfully for your/their protection, and I assume somewhere along the line they employ lawyers.
http://www.legislation.gov.uk/uksi/2000/2699/contents/made
http://www.foxwilliams.com/news/344/
In order to be lawful, the system controller* must have made all reasonable efforts to inform every user of the system that communications might be intercepted.
so it becomes a written policy and a condition of use – on just about every system in Thames Valley Police you have to click “Ok/yes” on a text box explaining this before proceeding, which means we have watertight proof the user was aware of the policy.
*And from the Act “system controller” is
“system controller” means, in relation to a particular telecommunication system, a person with a right to control its operation or use.
which probably means you as the “computer guy”.
You are doing the right thing in protecting children, you are also doing the right thing in trying to protect yourself and your employer and ensure the integrity of the work you do and any evidence you gather, but other people within the organisation should be doing this for you.