And rightly so! (I'm sure you agree now you're old and sensible!)
Tony is correct. We were instucted to decline ANY service to an untaxed vehicle except to remove said vehicle from a dangerous or obstructive position. If the wheels are touching the ground it's on the road and subject to vehicle regulations.
Carrying an untaxed/untested/uninsured vehicle is classed as goods in transit and may not be covered under your insurance for a recovery vehicle. If the 'load' drops off and kills someone you may be up that brown stream with no method of propulsion!