Hi James and welcome to the forum
Yes £1m is enough for domestic. Public liability is there to cover you in case you cause damage to someone's property while you're working, or injure someone.
If you damage someone's house or car, its hard to imagine it costing more than a few thousand poinds at most to put right.
However if you were to seriously injure somebody, or prevent them from doing their job, you would be liable for substantial compensation. Thankfully this is rare, but even in such a situation £1m is enough.
If you ever want to tender for public contracts, for example schools or council buildings, they usually require you to have £5m cover.
-Philip