I'm sorry you are in such a difficult situation.
The legislation already allows for people to travel to work, even where it is not 'essential' work. Many workplaces (not including certain industries like clothing retail, hospitality and leisure) never had to close. Travel to and from 'unessential' workplaces, where those workplaces were allowed to be open, was never prohibited.
There is obviously a broader and very important question about safe workplaces, and whether or not people can be compelled to attend what they might consider to be an unsafe workplace. I understand this is a really important issue that many people rightly feel very strongly about, but I wont go into that here.
The general impression I've taken from the media is that many employers seem to have taken the the 'stay at home' message to mean that none of their employees could come to work. They therefore furloughed everyone.
I think the government are now trying to clarify the original position about how they never intended for so many people to be kept off work (rightly or wrongly).
People who cannot work from home, but cannot attend their workplace because of childcare responsibilities, are still allowed to be furloughed. Hopefully employers will continue to use this option for people in your situation.
If your employer insists that you attend work, and you cannot as you do not have childcare, then yes you are in a very difficult situation.
You obviously cannot leave your children alone. If you refuse to attend work, and your employer refuses to furlough you, you may be able to take unpaid parental leave. You may be able to take annual leave, which would be paid but is obviously limited. Your employer may offer some other kind of unpaid leave.
Your employer may threaten disciplinary action if you do not return to work. They would (so long as you have 2 years service) have to go through a fair process before terminating your employment for your refusal to attend work. It would depend on all of the circumstances as to whether refusing to furlough an employee rather than dismissing them could be fair.
I really hope your employer is understanding, and makes use of the furlough scheme.