Hi and welcome to SAYNOTO0870.COM.
You can call so-called "freephone" numbers (0800/0808/0500) from your mobile using a dial through provider such as 020 0222 0900. Calls will be charged the same as a call to a geographical (landline) number as that is what it is.
Dial the number, when it answers, input the destination freephone number.
For the purpose of those reading this at a later date, today is Sunday. I tried the following numbers just now and found that they are closed:
01603 202500
01904 685000
0800 0686800
They all say they are open 8am-8pm M-F 8:30am-5pm Sat. I believe that these are for customer services.
Car insurance claims is also 0800 222400.