Rim brake bike with good stopping power needed.

An unusual request. Why do you need such power ?

Don't forget the tyres need to be thought of. If you're on narrow tyres it's very easy to lock them up. Wider fatter tyres have more grip on the road.

Never had any issues with any Shimano 11 speed brakes 105 or ultegra. 10 speed ultegra was a bit pap bit still pretty good.

I have found that Shimano calipers with SRAM levers to be by far the best combination.  I think toe in is a waste of time, once you have used your brakes a few times the pads will have worn parallel to the rim anyway so you will have lost any toe in.  Unless you reset the toe in every couple of rides there is no point and from my experience there is no improvement in braking performance anyway, Shimano recommend toe in of 0.5mm but I have never noticed any benefit from doing this.

Buy basically any Shimano equipped bike then buy a 105 or ultegra front brake either 5800 or 6800 or r7000 or r8000

or put some swissstop bxp on the front of whatever brake you get with the bike and toe them in properly 

"Apparently are fitted on bikes where the frame and wheels are in a good position" not sure what that means.

Anyhow, you get what you pay for. A cheap bike will have cheap(er) brakes. If you want powerful brakes you will probably have to upgrade them. You won't find a bike for £700 or less, brand new with top end brakes fitted.

It also depends what you mean by 'stronger braking than average'. Depends across what range of braking ability you are looking at. Surely you just need what is adequate for your intended use? If you are riding the Alps descending at 60mph often you will probably want a top quality brake, if you are riding in Norfolk you could probably accept much worse, but still perfectly adequate braking.

PP