Can't be done I'm afraid. Closest you can get is down to Market Harborough, but the Mkt H'boro arm of the Grand Union is narrow with the 10 narrow locks at Foxton and 7 at Watford stopping you getting to the Grand Union near Buckby. http://www.jim-shead.com/waterways/Inland-Wate rways-of-England.html
You could get across the Pennines on the leeds-liverpool and across the Mersey onto the weaver navigation but would still be reasonably stuck as the systems south of there are narrow.
But having got that far it might reduce the cost of road haulage to Bristol.