Kitchen/diner - roles of builder, kitchen company and interior designer

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There's some great advice on here. Thanks to everyone who contributes.

We're moving and the new house - west London victorian terraced - needs a new kitchen/diner. We want to add a downstairs loo and space for washing machine near the stairs but no other structural work would be needed.

2 questions. Am I right in thinking we need to talk to builder first, then a separate specific kitchen company? (is Magnet a terrible idea). If we'd like a bit of guidance on things like the colour palette, sofa, lighting etc when should an interior designer get involved?

Second question. The overall space is about 9.7m x 3.6M.

Including everything - flooring, lighting, kitchen, appliances, fitting etc etc is 30 - 35k ambitious?

I realise it's a bit how long is a piece of string and haven't got a clue yet about the flooring which can obviously make a big difference but if we're assuming kind of mid level pricing for things is that kind of budget going to work?

I knew the kitchen I wanted and designed it all myself (from DIY kitchens - don’t let the name deter you, have a look ) so first I found a joiner who would fit it. He brought in all the trades - builder, plumber, electrician, plasterer, painter.
I sourced the bifolds, sink, quooker, worktops and he liaised with them all to get the work done on a schedule. He was ace.
Oh and I had to sort building regs, survey etc for the building work

You need oneplan from Houzz - she works with you to design it and then you shop around with the plans. John Lewis do nice kitchens. Lots of smaller retailers need business so I'd be tempted to try them too. At least if they all price the same plan you can compare properly.