The first suggestions I read regarded the /etc/network/interface file which I modified thus (I renamed it when I could not get it to work):
I experimented with the ssid or the wpa_supplicant.conf file (which referenced that ssid) but ifup had problems with both.pi@raspberrypi ~ $ cat /etc/network/interfaces.man
iface lo inet loopback
iface eth0 inet dhcp
iface wlan0 inet manual
#iface default inet dhcp
Then I read about wicd which I installed. I set up the static address 10.1.1.91 as above, defined netmask, gateway and DNS server, used wicd to disconnect/connect and all was good - I had the address set up how I wanted it. I ticked the box to "automatically connect" and rebooted.
After the reboot the wireless connection was active but it had lapsed back to the DHCP address allocated before - 10.1.1.101.
So...any recommendations for the configuration of /etc/network/interface? Or, is there anything I missed out in wicd?