OK. I have done some more looking and now put my money where my mouth is.
While I believe the Vonets is a goer to put Arduino onto WiFi, I think this is a better bethttp://www.ebay.com.au/itm/300Mbps-300M-Mini-Wireless-WiFi-Router-Repeater-Network-Range-Expander-Amplifier-/350786460622?pt=LH_DefaultDomain_15&hash=item51ac809bce
and I have just bought one.
While the Vonets has the right purpose, it appears to be single purpose. This device is multi-purpose, incorporates its power supply and is generally better thought out - all for just a few dollars more. I buy it reasonably secure in the knowledge that, if it won't deliver for the Arduino, I can use it as a repeater. This means I should be able to use my crappy tablet, which actually has an excellent email facility, at breakfast outdoors.
I believe this device is a Baiyuyi but goes under at least one other name - Satechi. I also believe it is a tarted-up version of the crescent-shaped repeater seen a lot on eBay. It appears that the vital words in the technical description are "client mode" which, simply put, implies that it adds wifi capability to a swag of network-ready devices - like an Arduino+Ethernet shield.
Within the limits of my expertise I was planning to have a Uno talk via NRF24 to a Mega which is connected to the Internet. The Baiyuyi forces a re-think of just about everything but there is one essential goal - to get the data up on Xively. If the Baiyuyi works, it means I can do the job with just one Arduino.