Recently opened an account with http://www.18185.co.uk and can call 0844, 0845 and 0870 numbers from my mobile for 3p per minute. You can view your itemised calls online, seems to good to be true. Been using it for a while with no problems.

Also calling 0800 from your mobile is FREE using your free minutes. Call 01243 590800 and then enter the 0800 number

Have a look at reply#23 on this thread........

http://www.saynoto0870.com/cgi-bin/forum/YaBB.cgi?num=1296840243/24#24

videospy wrote on Mar 31^st, 2011 at 7:51pm:

Recently opened an account with http://www.18185.co.uk and can call 0844, 0845 and 0870 numbers from my mobile for 3p per minute. You can view your itemised calls online, seems to good to be true. Been using it for a while with no problems. Also calling 0800 from your mobile is FREE using your free minutes. Call 01243 590800 and then enter the 0800 number

You cant call 0844 numbers from 18185. 0845/0870 yes but not 0844
I have been using it  for years both from landlines and mobiles  and experienced no real  problems.

Its recommended by many including MSE http://www.moneysavingexpert.com/phones/free-international-mobile-call and http://www.moneysavingexpert.com/phones/cheap-calls-to-mobiles

And this very site http://www.saynoto0870.com/calls.php  

The access number 01243 590800 is a relative newcomer.

You have been able to use geographical access numbers like

Pre-Dial,s:  0200-222-0700 or  0200-222-0900
QX Dial,s : 01635-774-305 or 01635-774-325

to make calls to freephone numbers 0500/0800/0808 from your inclusive not free minutes , for some years.

Thanks. This is exactly what I was looking for. Saynoto0870 is not necessarily available when I have no access to the internet or for the 0845s/0870s not listed thereon (One of my clients has an 0845 number for VOIP every extension in their business!)
However I still have not found the answer to one issue. When abroad and calling from a landline, telephone companies charge ridiculous prices for phoning UK 0845s - when there is no equivalent geographic number the cheapest I have found is to phone the UK access number for the Tesco or Post Office calling cards and then pay 4 or 8p/min for the call. Anyone any other ideas