You should be able to get day work (which may include starts as early as 4am btw). There is quite a lot of night work on C+E, but there always seems to be a fair number of drivers willing to take those shifts / jobs, for whatever reason, be it quiet roads, better pay, peace and quiet etc etc. Apparently it becomes normal to be up at night.
There doesn’t seem like a reason to accept a job doing shifts covering a large part of the day (vastly different start times etc). Professions where this is the norm would have significant shift allowances.
Never fall for any argument put forward to the effect of: ‘it is legal, therefore we would expect you to do it’.