Loopy my 12yo travels 2 hours to/ from London every week and also crosses London on the tube by herself. My other DCs also flew as accompanied minors from age 8. Your DCs will be fine.
The flight as accompanied minors will be more structured than the train, there is less to go wrong as they will be accompanied right through. We have had a few issues over the winter with the trains, cancellations and the like with bad weather. The worst was when the whole east coast line was closed and we had to find a way to get her from London to Yorkshire. But if you put them on the train and they are met at the end you won't have a problem.
You can follow their train journey online at National Rail.com or on the train companies website. It gives all information about lateness, disruptions and line problems. The train companies also have twitter accounts which has been invaluable for us.
My tips for the train are-
Avoid journey times when people are travelling to/from football matches. It can get rowdy, swearing/drunks. This is mainly Saturdays. Saturday evening in particular.
Sit in a busy carriage, you can book their seats online. Book them as a two rather than on a table seat. They don't have to sit with strangers then.
Make sure mobile phones are charged, most trains have seat sockets too.
Make sure they have money.
If there is a problem, tell them to find the guard or station staff if they are offloaded ( if train breaks down for example.) the staff will sort out an onward journey, they will not have to pay for another ticket.
If you book way in advance ( up to 3 months) consider booking them into first class. If you do this early enough certain train times fares off peak will be cheaper than a standard ticket only booked a week or two in advance. Those carriages are more heavily staffed as people are coming through serving food and drinks all the time. Search National Rail for this.