Good morning Peter, you will be better off employing a firm that specialises in repointing. They will have the correct raking out equipment and of course they carry this work out day to day, practice makes perfect.
Depending on your location in the country you should expect to pay somewhere between £40 to £70 per meter squared. Different styles and materials are charged at different rates.
Very tough to quote without seeing.
Ideally a brick layer is suitable for this work, however other trades like us would carry this out also and we are a roofing & maintenance business.
Hopefully that helps.
Manor roofing repairs