+1 for Jaeger if you can get to a factory shop.
Next do a ‘premium’ range of suits made with really good Italian cloth which are pretty good value for money. I’ve never seen them in store but you can get them delivered next day in to store if you want. For some unknown reason though the regular length trousers are 31″ long.
I’ve never found TM Lewin staff to be snooty, their suits are again pretty good value for money – have a stitched canvas rather than bonded so if you need to get them adjusted it’s not too much hassle.
Never been to Slaters, may have to try it.
Where about do you live? If you’re interested I use a tailor who can make you a bespoke, made to measure a suit for around £600-700 depending on cloth.