I have a rescue cat (boy age 3 1/2) - he climbs my brick walls, neighbours roofs - no issues at all!! I had been told by the rescue charity about a loop thing that goes around the garden and fits on the cats collar. I've decided not to install and keep the cat in at night and when I am out all day.
All of my outside cats would have been able to/have in fact scaled brick walls as high as that with no apparent difficulty if eg in hot pursuit. (They sort of take a run at them and just 'Zoooopppp' and up. What seems to be important is what's at the top because their momentum carries them up there.)
Given the expense of brick walls (have you costed them ????!!!), I'd be thinking something else.
We've recently moved to a house where our cats could get out onto the road (quiet cul-de-sac, but still...they're fairly dim and as they're rescue cats we don't know their history so could have no experience of cars at all).
Anyway, we're looking at various cat proofing methods. One company came round and planned out a system to be fixed to fence, and they said there was no need to fix cat-proofing to a brick built extension and outhouse we have as they wouldn't be able to scale the brick wall.
Which has got me thinking - could we acheive more aesthetically pleasing cat-proofing just by walling the entire garden? Possibly prohibitively expensive, but that aside our garden would really suit it. It would look great and if it would work would be a win-win. The cat proofing isn't at all pretty.
Can't find any conclusive info - the cat proofing company guarantee their system is effective, which suggests they are 100% confident cats can't get up 6-7ft brick walls. My parents have a walled garden and I've never seen a cat get up or down that in 25 years except at one point where there's something about 3 ft against it to create a jumping point. But I've come across a few comments online saying cats can scale brick walls.
(I have very large, fairly ungainly middle aged ladies, btw, not lithe acrobats).