Upvote:-3
If you are a British citizen, then your children are too, whether they want to be or not. If this is going to be a frequent problem in the future, it may be time to get them British passports. It takes time and trouble, but when it's done they are Europeans.
(Unless the UK leaves the EU in the meantime, of course.)
Here is the official site: https://www.gov.uk/government/publications/chapter-20-british-citizenship-by-descent-and-otherwise-than-by-descent-nationality-instructions
And I hope I am allowed to mention here that Wikipedia has a lot of useful links too.
Upvote:4
It seems to me your children did the right thing as they submitted everything they should/could. But if the amount of money is not enough for the trip (see @pnuts' comment for some details), the consulate also did the right thing by refusing to issue the visa. Since your children are travelling alone this time, they are not covered by EU freedom of movement rules and your being a British citizen is not directly relevant so it's not unexpected that getting a visa would be more difficult.
The reason for the refusal is straightforward and the obvious solution is to get (or show that you have) more money. Some documentation of your finances (pay stubs, bank statementβ¦) and a statement that you would pay for living expenses (not unusual for children, certainly for minors) should help. Without that, the consulate only has your word and GBP 800 for two people, which might not be enough to meet their guidelines.
I don't know about this document for minors travelling alone, the consulate can presumably help you with that.
Once you have all that, the only practical course of action at this point is to start a fresh application.