There are two problems here, the first being how to remove the old paint and the second what to replace it with.
Before going down those routes however we would strongly advise checking with the planning office, if you haven’t already done so, as to whether having a painted finish is still a requirement for the area. If it isn’t, then some simpler solutions might present themselves.
Removing Old Paint From Bricks
Assuming this is still the case then we turn to the problem of removing the old surface paint without damaging the bricks. If the bricks are indeed engineering bricks then they will be denser and harder than normal building bricks, so they may be easier to clean without being damaged.
However, engineering bricks are not often used to build domestic houses as they are uglier than house bricks, more expensive and unnecessary. They will occasionally be used for retaining walls and damp-proof courses, but rarely a whole house.
It would be wisest to assume the bricks are ordinary and proceed with the least damaging method of paint removal which is a power washer. This should get the worst of the flaking paint off.
Trying More Aggressive Tactics
You could then try a chemical stripper or sand blasting to get the rest of the paint off. Sand basting can be very messy and with a chemical stripper you need to be sure that you get all of it off or the new covering may not stick properly.
With all of these solutions, including the power washer, try them on a small innocuous patch first and make sure that the brick and mortar are not damaged before you continue. Also bear in mind that you may not have to remove all the paint from the brick walls. With some coverings once you’ve got the loose flakes off the surface good enough to reapply paint or a textured covering.
Choosing New Paint
The new surface covering can be paint, render, or any number of commercial textured surfaces. There are too many different options to cover here but if there are similar houses in the area, particularly if they are constructed with the same sort of brick, the best option would be to go round the area asking people what products they’ve used and how long they last.
If you can’t get any decent recommendations that way then consider getting one firm to remove the old paint removal and the new surface. Then if there are problems a few years down the line, you’ll only have one company to deal with. If you use two companies, they could end up blaming each other and you’ll be left in the lurch.