Having found the Geographical number for a company (eg Tesco) how can I stop them "blocking" me because I am ringing from the UK? how can I withold the CLI - whatever that is?

Tesco now uses a mix of 03 and 080 numbers.

http://www.tesco.com/help/contact/
http://www.tesco.com/store-locator/uk/asp/towns/?l=L&t=LONDON
http://www.tescobank.com/help/contact_us.html

Calls to 03 numbers cost the same as calling 01 and 02 numbers and count towards inclusive allowances on landlines and on mobiles.

Calls to 080 numbers are free from landlines and from mobiles.

There is generally no longer a need to use workarounds.

If you do ever need to withhold your number, the usual method is to dial 141 before the number you are calling.

Ian01 wrote on Jul 14^th, 2015 at 5:40pm:

… If you do ever need to withhold your number, the usual method is to dial 141 before the number you are calling.

If an organisation is seeking to handle calls from different locations differently, it should be using the caller location identity, which is separate from the CLI. Because this does not identify the specific caller in any way, there is no privacy requirement to allow it to be withheld.

The point is fairly made that SayNoTo0870.com may need to re-focus its efforts on avoiding charges for accessing genuine premium services, as the campaign against unfair imposition of Service Charges on 084/087 numbers is finally achieving considerable success - 'SayNoToPayingFor09' perhaps!  ;).

'SayNoTo070' and 'SayNoTo076' could have a short lifespan, because Ofcom's attention is now on these ranges; with the hope of action once the present phase of activity has calmed down.

"Saynoto0870" essentially ceased to be relevant on 1 August 2009  - listen here to hear the principles of what has now replaced that misguided, incomplete and unduly selective Ofcom move being outlined at that time. The need to correct that error is perhaps seen most clearly in the reinstatement of revenue sharing through Service Charges on the 0870 range.