There are moorings on the Upper Avon (ie above Evesham) by many of the locks.
Decent moorings in Evesham and Pershore. Asda in Pershore is close to the moorings and a good place to stock up.
Moorings in Tewkesbury at the Marina, or near Avon Lock (fees for both).
On the Severn, most of the pubs have moorings, and there's a BW pontoon at Haw Bridge.
Check tides on the Severn below Tewkesbury here:
http://www.bbc.co.uk/weather/coast_and_sea/tide_tables/12/522a
Anything more than roughly 8 metres will overtop the weirs at Llanthony and Maisemore.
If a tide is due, speak with the lockies at Gloucester or Upper Lode for timing. They won't usually let you through if a big tide is due as it often brings a lot of floating debris with it.
Upper Lode Lock 01684 293138 Gloucester Lock 01452 310832
Going downstream you need to speak to Gloucester lock before you enter the Parting - there's a big sign with the phone number, or VHF Channel 74.
On the G&S in Gloucester, the moorings between Sainsbury's and Monk Meadow dock are 14-day.
Plenty of VM's on the G&S.