Canal & River Trust have a useful map: https://canalrivertrust.org.uk/in-your-area. Icons can be set to show links to many features including boating holidays, moorings and services.

Offa's Dyke path heading north from Hay on Wye or Knighton finishing at Trevor on the LLangollen canal by Pont Cysyllte aqueduct,

Stewart Brady

You could hire a boat from stourport on severn or Kidderminster and do numerous walks from that location . The worcestshire way , North Worcestershire path, monarchs way, severn way to name a few , also the carpet baggers anytime challenge is very nice . The staffordshire and Worcestershire canal is lovely lots of canal side pubs that serve great local ale and super food . Wolverley , kinver also beatiful villages which the canal goes through
You won't be disappointed

The Cotswold Way National Trail is the obvious one - there are several companies that provide accommodation packages for it (Google them) and the southern end is in Bath (itself worth a day or two's exploration) which gives you access to the Kennet and Avon Canal. At least one narrowboat hire company has a base there (AngloWelsh) and there are probably others.

Failing that you could always try Norfolk, though there really isn't a single contiguous trail that can provide a week's entertainment .....

My wife and I would like to spend a few weeks in the UK next spring. It will be our 1st time and want to do everything. The two things we want to do after a guided tour of the country, is to take a week for a LD walk and then take a week for a narrow boat tour.

Are there any walks that start or end at a narrowboat rental?