Are road tyres suitable for any off-road riding at all? I'm looking to buy a bike for my commute - 6 miles a day. The commute itself is all on roads, so naturally I'm looking at road bikes. My main worry is that if I invest in such a bike I won't be able to ride off-road at all, for example down a towpath (Towpaths can have very rough surfaces). 

Would I be better off investing in a light hybrid bike (with thicker tyres) over the road bike, given that I might want to go off-road some of the time?
If you're looking for a general purpose bike for commuting and towpath riding, you probably want to avoid a standard road bike, they are very specialized and have very small tire clearance.  Typically supporting tires no larger than 28mm and often lack mud guards or rack/pannier mounts.

However, touring bikes or steel cyclocross bikes (if they have rack and fender mounts), tend to be great choices for those purposes.  Both will often have clearance for tires up to 35mm or larger which you can use for off road riding and have a more traditional road geometry versus the more upright hybrid geometry.  However, if you prefer the more upright stance and flat bars, then a hybrid may be more well suited to you.  

I would make sure that whatever bike you get does have rack/fender mounts if it's going to be used as a commuter.  You never know if you'll want to start using a rack and panniers to carry your gear off your back or fenders to keep you drier in the rain.

You can get knobby tires for any of these bikes, but I would stick with high quality, puncture resistant road tires wider than 28mm.  Even slick tires that are 35mm should be fine for towpath riding, I wouldn't take them on singletrack though.