I had this same problem the other month & it caused a full tank to last just 65 miles.......
The prime suspect is usually a bit of crud in the float chamber jet, which is stopping the float closing the valve that shuts off the fuel flow. It could also be a damaged jet or jet valve seat, but most likely to be crud
You'll need to remove the float chamber lid from the carb, and then very gently knock out the small bar that holds the float chamber to the lid - it will normally only go one way - look to see where the knurled end is. Once that is off, the jet can then be lifted out for inspection, & cleaning of the seat. Reassembly is the reverse of disassembly, except you swear in different places
I'd also recommend replacing all the underbonnet fuel hoses and fitting a fuel filter, in case the problem is being caused by the innards of the old hoses breaking up.
Hope this helps