Would I replace the +44 part with 07 or just 0?
+44 is just the 0
The +44 indicates to callers anywhere in the world that it is a UK number which has an international dialling code of 44.
If you want to dial an international number from the UK we use 010 plus the International dialling code for whatever country you want. So for example a German number might be shown as +49 which we would dial 010 49 from the UK.
The +xx format is used because not all countries have a prefix of 010 for international numbers - many require 00 for example so this format of showing numbers is very useful.
To make things easier for us most mobile phones allow you to enter the +44 as it is written and it will use whatever prefix is needed in whatever country you are in.
In my phone I have all numbers entered with +44 (or the relevant international code if they are not UK based) so they work wherever I am.
If you don't want to do this then as others have said put 0 in front of the number (ignoring the +44) but this may not let you reach the UK number if you are abroad.
Hope the additional information is of interest and use.
Yet again this question is asked and yet again I am surprised at all the wrong answers that are given.
+44 is the european standard international direct dialling code for the UK.
The + sign is equivelant to putting 00 before the country code not 010 as steve has said.
If calling from outside the UK you would dial
+(00) 44(UK) 1234 567890 (first 0 of number omitted).
To correct steve's example it would be
+(00) 49(Germany) 1234 567890.
The only exception to this is if calling from USA or Canada where the 00 is replaced with 011.
Just the 0. Same thing applies for non-mobile numbers too
It just means the 0. For example, a number that is displayed as +44794, etc would be redone as 0794, etc. The same applies with landline numbers, where a code beginning +4412, would be redone as 012, etc.