0370 are numbers used by government agencies and businesses which are not linked to a specific area of the UK. They are a fairly new type of number, introduced in 2007. They are also called NGN or Non-Geographical Number. Although introduced to assist landline users by keeping charges constant these numbers are more often nowadays used by mobile phone users.
From any mobile, whether a smartphone or more usual mobile phone the charges for an 0370 number is charged the same as an 01 or 02 number. This is only an approximate number and your mobile provider can give you more information. It may be more expensive if you call from abroad, although some mobile phone providers do not charge roaming fees, again it is best to check with them.