Hi Stephen and Kate,
I lived in Worcester for 21 years and kept a boat there. The river is quite OK to moor on provided that there is not a rain deluge forecast. I think you will be OK for a few days. The race course moorings are OK but don't moor under the footbridge. The city might send a minion round for a few quid fee....then again they might not!!
The alternative is to lock up onto the Worcs/B'ham canal and use the visitor moorings. The locks are large and the gates heavy, but as you're going to do this anyway it might be worth it. There are visitor moorings plus water and pump out. Easy access to the city etc. I loved living there and hope you enjoy it.
To enter the locks off the river do NOT try to turn straight in to the lock, rather go past, turn (plenty of room) and then go on to the the lock pontoon.
Enjoy.
Tim