What is a suitable mortar when repointing a wall made of soft red brick?
Please don't let a cement based mortar go anywhere near your house! Definitely use a lime based mortar. I won't get into specifics as it's very location dependent, but a quick google search of the options available in your area should find a nearby supplier. Usually either a tubbed putty or a bagged powder mixed with sand or if you're lucky, a complete pre-mixed mortar ready to use from the tub after a mixing to liven it up.
A basic lime:course sand mix would be around 1 lime to 3 sand. Sometimes a little stronger 1:2.5 or so.
The sand needs to be clean and well graded, not too many large stones/grit. I sieve my locally available sand as it's mostly a little too coarse for the fine joints I encounter.
It's a big subject though, with more than a few do's and don'ts. Firstly make sure the joints are actually ready for re-pointing. If you need to rake out lots of mortar to get a nice deep joint then maybe it can wait a few years (cracks excepted).
Secondly, clean out the joints and moisten them well before packing in the dryish mortar. Keep the finished pointing protected and damp for a week or more. Slower the better.
There is some good stuff on the thisoldhouse dot com website.