Thanks, kobra, I've set up the zones as detailed below:

Zone Based Rates
Enable Zones Method
True
Calculation Method
Price
Tax Class
--none--
Tax Basis
Shipping
Sort Order
10
Zone 1 Countries
GB
Zone 1 Shipping Table
10:1.95,10000:0.00
Zone 1 Handling Fee
0
Zone 2 Countries
00
Zone 2 Shipping Table
1000:4.95
Zone 2 Handling Fee
0

At checkout, I get this message:

Not Available At This Time Sorry, we are not shipping to your region at this time.
Please contact us for alternate arrangements.

There's obviously still a problem somewhere but I can't work out where.

I'd be grateful for further suggestions.

Thanks.