Piglet. Highams work are individually made pieces of furniture. Solid wood
And no chipboard or laminated anything. They build high end bespoke solid wood furniture.
Eg. My island is 1200mm x 2400mm and is made up of three separate pieces of furniture.
This isn't the flat pack stuff you buy from Magnet or second nature etc.
Completely bespoke. They can build you anything you wish for.
OP I have a Higham kitchen. The handle less shaker. Stunning durable and fantastic.
Mine was featured in an interiors magazine not long ago (ask them and you can have a look
).
In terms of price. There are ways to lowering the cost. Have fewer drawers.
Big pan drawers are a pain. You fill them with crap and they look untidy when you open them.
To save I ditched all the drawers from my island and have cupboards in stead. It's fab.
I do have two pan drawers at the bottom of my dresser/drawer. I don't use them. One is empty and the other has tea towels in.
Kitchens been in for two year and it's still beautiful. Pretty indestructible despite having a 3 and a 5 year old. 
Tall units are expensive too.
It's very hard to say where your most expensive items are without seeing your plans and layout.
Pm me if you like and happy to help. If you want me to look at you plan. I'd happily do that too.
Did you ask about discount at all? Sometimes they will offer a few % off (don't tell them I said that).
Also their fitting costs may seem high. However their installation was second to none. And aftercare. I had a hinge break (DS and DD involved)
I only called to ask where I could get an exact match but they sent someone from their workshop and refitted the door.
Wasn't their fault my DC were using the low unit doors to hang on and swing. 
You could also make changes to your plan/layout to save. Again can't be specific without more detail.