We have re entry done our bathroom and I sourced everything myself. Had the same view as you that I would rather get good quality brands at byrne prices. In general I looked for brands I liked and then narrowed it down to a style and then just searched Google for the best price. Remember to compare the delivery cost too as sometimes for large items it can be very high, the price for the item might be slightly higher elsewhere but with free shipping.
I got our floortiles form Harvey Maria, I love them but they've only been down a week and already have a few little scratches! So time will tell how well they last.
Got our wall tiles from Tile Mountain who were AMAZING. I got so many samples from so many places and theirs were by far the nicest and best prices by a long shot. Customer service excellent too.
Shower and taps for sink and bath are Grohe. Hansgrohe v good too but were over budget. Crosswater, bristan and another which is escaping me right now!
We got a simpsons shower enclosure as we needed quite a specific size/shape that is less common so had to get quite a pricey one. It was from CP Hart who's customer service was Shocking. I would never use them again.
We got the bath, towel rail, shower tray from Victorian Plumbing. I avoided them at first but they were actuall very good, and have loads of lovely brands like Burlington etc.
I got a lovely mirror from Soak that I was v happy with.
We had our vanity unit made by Harvey George. They have a website but I originally found them on eBay as they have a shop there. They were very good, good price and very patient with my endless questions.
Toilets - we picked a generic one from Victorian plumbing but we are doing our en suite soon and I will be getting a branded one for that I think. Looking at Duravit, v&b, Bauhaus, etc but looking at extra display on Ebay or previous styles for a bit cheaper. If you need a concealed cistern the plumber said he would only ever fit gerberit as they're the best and most reliable.
Good luck! you'll realise as soon as you start researching that it's a bit of a minefield. But it's worth it in the end!!