I think there is a big issue where people who could and should be working were furloughed by their companies instead.
It was never intended for everyone but essential workers to stay home, is was intended that you continued to go to work, from home if you could, but if not possible , then at your place of work. The furlough scheme was originially intended for those companies who needed to shut - e.g. hospitality, non essential retail, entertainment etc. Things like office based work, manufacturing etc should have all continued, but many chose to shut and furlough staff.
The plus side to this is that this will have helped control the spread of the virus. The downside is that its just not financially sustainable.
I think there need to be clearer guidelines around who can/can't be furloughed, and it really needs to move to a basis whereby its for employees of businesses that the government have actively asked to close only. Childcare is an issue, but I don't think its one that should be covered by furlough. I'd perhaps like to see some additional legislation around (unpaid) parental leave - perhaps a law passed that allows one parent of a family with children under 10 to take unpaid parental leave from when furlough is lifted until the end of the year with the right to go back to the same job etc (like additional mat leave). Perhaps something about the right to ask for flexible hours too, so that parents could work around each other where that is possible. Nannies/childminders should still be able to work, and even nurseries could operate with limits on the number of children per room/setting. This would be a way to gradually ease of lockdown.
Obviously socially we still need to remain in lockdown, the things that should be relaxed are those which allow the country to function economically and get things back up and running.