Why paint is a problem
Cement render bonds mechanically. It works by getting into the pores and texture of a masonry surface and gripping. That is the entire mechanism.
Paint seals those pores completely. When you render over a painted wall, the render is not bonding to the brick at all. It is bonding to a thin film of paint, and that paint film is bonding to a brick that has been sealed for however many years.
So the strength of the whole system is now the strength of the weakest link in it, which is the adhesion of a decades old paint film. Add the weight of ten to fifteen millimetres of render, plus thermal movement, plus any moisture that finds its way behind, and it lets go.
What failure actually looks like
It is rarely immediate, which is the frustrating part. A render over paint usually looks perfect for the first year or two.
Then you start hearing a hollow note when you tap parts of the wall. Then a hairline crack appears, usually along a corner or an edge. Then after a decent run of wet weather, a section comes away, and it comes away in a sheet with the paint still stuck to the back of it.
By that point you are paying for demolition, disposal, substrate repair and a full re render. It is the most expensive way to save money in this trade.

Option one: remove the paint
The most reliable approach is to get back to a bare, porous, mechanically sound brick surface. There are a few ways to do it.
Mechanical grinding or wire cup brushing works and is precise, but it is slow and dusty. Abrasive blasting is faster on large areas but it is aggressive and it can damage soft brick, so it is not appropriate on older sandstock. Chemical strippers work well on some paint systems and poorly on others, and they need careful containment and disposal.
Whichever method is used, the wall then needs washing down thoroughly and drying before render goes on. Budget a genuine cost increase for this. Paint removal is slow, dusty, labour heavy work and it can add half again to the cost of the render itself.
Option two: a bonding bridge system
The alternative is to leave the paint and use a product specifically engineered to bond to sealed, non porous surfaces. These are typically polymer or acrylic modified slurries that grip the paint chemically rather than mechanically, and give the render a keyed surface to hold onto.
Done with the right product and correct preparation, this works well and it is much faster and cleaner than stripping. It is also more expensive in materials.
The critical condition is that the existing paint has to be sound. If the paint is already flaking, chalking or blistering anywhere, a bonding system just attaches your new render to paint that was on its way off. In that case there is no shortcut, the paint has to go.
The test you can do yourself
Before you get quotes, do this. Take a roll of strong packing tape, press a strip firmly onto a few different areas of the painted wall, and rip it off quickly.
If the tape comes away clean, the paint is well bonded and a bonding bridge system is likely viable. If the tape lifts flakes of paint, the paint is failing and it needs to come off.
Also run a hand over the wall. If it leaves a chalky residue on your palm, the paint has broken down under UV and it will not hold anything.
What to ask a renderer quoting your painted wall
This is the single most useful question you can ask when comparing quotes on a painted house: how are you dealing with the paint?
A renderer who has scoped the job properly will tell you whether they are stripping it or bonding over it, which product they are using, and why. A quote that does not mention the paint at all has either not noticed it, which is worrying, or is planning to render straight over it, which is worse.
There is one more option worth knowing about. If the paint is sound and you mainly want a fresh look rather than a flat wall, a texture coat over the existing paint is often a legitimate and much cheaper alternative to rendering at all.
