The key to selling anything luxury / custom is to sell the dream to the customer. Or 'sell the sizzle' as
@MBE2017 suggested.
They are not just buying a piece of furniture. They are buying a centrepiece for their home, room or garden that incorporates craftsmanship that has been developed over two generations.
Don't underestimate the story of you and your father. They are also buying into you and the story behind your business, as much as the item itself.
Your knowledge of 'optical polishing, lens making, aeronautical engineering, photography, joinery and now cabinet making' is an incredibly powerful background. Use it.
At the end of the day, they are buying into the 'feeling' of owning something special that nobody else or very few people own. This is what a luxury brand is.
My suggestions on the site would be as follows:
Tell the story - As some of the peeps here have said, create a video to talk about your history, knowledge, experience and passion for perfection. This can go on the homepage and hook people before they even see the products. Look at watchmakers. People buy into the heritage, story and brand before they even decide on the watch they want.
Create videos for the products - Explain what makes them special and communicate the thought and process that has gone into creating it. This is where and how they will see the value. Also, talk about its exclusivity because scarcity is a powerful marketing strategy.
Homepage - This needs more impact. I think the drawers seem to be a more interesting piece so I would bring them to the forefront. You should also give a little intro to you that feeds into your about page. Personally, I would create a page that talks about your process, from concept-to-creation. People want to know this. Remember though, the homepage is NOT a sales page. It's a hook page to get people in, just like a shop window.
Gallery - Is there a gallery or your previous work? This could generate requests for custom work and further your credibility.
Navigation - You only have a few products and we are trying to go premium here. I would have a simple navigation menu that says 'Collection'. That way, people will see all your products in one go instead of navigating to a page to see one product in a collection. That's not a greater experience.
Customer Testimonials - Do you have anything that people have said about your work? These could be presented in a premium way and creates credibility.
Product Descriptions - These need to be far more luxurious and go into detail about how it was created. For example, you want me to part with £1200 for the Arietty Small Drawers. I haven't got a problem with that but you need to sell it to me and demonstrate why it's worth that much. In my mind, every product has a story to tell.
Imagery - These are good but I need more detail. Feet, insides, finish, and textures, handles, etc. I want to see every angle.
Video - I've mentioned this already. Video is the best converting tool on a website if done right.
About Page - I want to see you, your Dad, the team and the people behind it. You should be positioning yourselves as 'artisans' of your trade. The entire brand revolves around your skills, knowledge and attention to detail.
Font - I don't think the font you are using exudes luxury. It looks too basic and not premium. I know it's a Squarespace website but they must have something better.
Blog - Your blog is your personality and lets people into your world. You need to create one (possibly called 'The Workshop') where you share the projects you are working on, your inspirations, customer case studies, etc. This will also help you to attract organic traffic through SEO.
Here's a couple of examples of how unique, high-quality products are being presented perfectly to create desire.
https://www.bagigia.com/
https://www.hardgraft.com/
Other Marketing Suggestions
In terms of marketing, think about the type of avenues where your products would be appreciated. You need to go where your audience 'hangs out'.
Instagram is a good channel to focus on because it's design-led and people with money do use it to find inspiration. But, you need to think about what content you post and the hashtags you use. Don't try to go for tags that have millions of posts because you won't be seen. Go niche, like #luxuryfurniture, #furnituredesign #furnituremaker #luxuryhomedecor, etc.
Also, research local hashtags to get on the radar of local press and customers. People love to support anything local. This is a big one. There are customers on your doorstep.
Another point about Instagram is that you need to be proactive and don't think that people are going to find you. You need to be seen. That means liking and commenting on posts from your potential audience and partners (resellers, press, etc). You need to build relationships with people before they will take notice. I've seen a strategy of 20 likes and 10 comments per day work. Make this your daily routine.
I don't see eBay or Etsy as the answer. I think you will have greater success networking with interior designers and trying to get featured on niche design blogs and home decor publications. If you've got interesting products (which you have) and a great story (which you could have), then it's possible they will feature you without paying.
DO NOT PAY TO ADVERTISE because you don't need to. Journalists and writers are always looking for content. I'm not saying this is easy because it's not. It will require hard work and patience but you only need 1-2 pieces of coverage in front of the right audience to get the ball rolling.
Steer clear of paid ads on Facebook, Instagram or Google because you will burn through money. Invest time or pay somebody (a student or social content junior) to help you create the content that will build your brand. It won't happen overnight but it can happen quickly if you put in the hard yards at the start and adopt the right strategy.
Hope that helps.
Matt