If you approach builders without drawings they seem a bit reluctant to come out and quote (guess they get a lot of time wasters). If you do get them to come and give a rough quote and you decide to go with them then you can use their preferred architect which seems to make sense since there can be less scope for blame later if they say the drawings were not quite right etc.
Conversely, getting an architect to do the drawings first seems worse. They may well do a great design but then if the builder quotes beyond your budget for that then you have to go back to architect and ask them to scale it down (which costs more fees). Then the builder might not be happy with the architects drawings and it leaves you open to being the middle man. I realise the initial quote can still vary a little bit until the final plans are drawn but surely this approach is more likely to control that.
So, is it normal to get the builder out first, tell your budget, get a quote, if it's agreeable then to say ok we will use your preferred architect and then go from there?