Unfortunately 12 is a really bad age to try and do this - unless your child has literally just turned 12, is tiny and young looking for age (eg. looks 9/10 and is about 4ft 8" max) and/or has a very particular look or ethnicity.
Children need to have a licence in the UK to perform and that means time and costs for productions as they also need chaperones, tutors etc. There are almost no roles in screen for 12-15 year olds and those that there are tend to go to young-looking, small 16 year olds who can play down and don't require a licence or any of the other things.
In terms of agencies, it doesn't matter where you live in relation to the agent as the chances are you will never actually meet.
What you do need is a parent with absolute flexibility and a decent amount of disposable income. You will need a Spotlight account (£114 a year), professional headshots (anything from £70-£350 a year), a self-tape set up (tripod, backdrop, possibly lights and mic, editing software and a quiet space in which to do these) and ability to travel at the drop of a hat.
Once you have been accepted by an agency (no easy feat - at 12 they will generally want a child with training and credits), you'll generally hear nothing for weeks and then suddenly get an email with a tape request/audition request. This can need turnaround in anything from 12-36 hours. Once tape is sent back then you will almost certainly never hear another word. You could get one tape in a month, or nothing for 6 months, or you could have nine in a week - or end up needing a week off work & school because of day after day of recalls. You don't get to say no to things either unless there is an extremely good reason (eg material in the script is controversial and this has already been flagged by casting) unless you want a v annoyed agent.
If you do win the lottery in terms of a recall then it's either another tape, or you'll need to drop everything and go into London at short notice. Generally auditions are after school, but you'll have to take them out of school in order to get to London for 4.30pm or whatever time you are sent. 5 mins in the room and again you will almost certainly never hear again.
You basically never get feedback and you never get a no. After 2-3 weeks you just write it off. Once in a blue moon, the stars align and then you have a whole new set of things to negotiate!
We've been doing this for over 10 years now, and even with huge amounts of training, West End and screen credits and a top tier agent, it's incredibly hard and a lot of work for both child and parent with mainly disappointment at the end. Someone once told me that booking 1 job in every 50 auditions is a good rule of thumb. Luckily for DD I had no clue what I was letting myself in for when we started - and I have an extremely flexible job.
Supporting Artist work (what used to be called 'extras') is completely different from acting. Some people enjoy doing it, but it is not credited and should never go on an acting cv nor does it count towards Spotlight qualifying credits.
If your DD is serious about acting, then the best bet is to look into getting some decent training across stage and screen genres and aim for things like NYT at 14.