Like Felix said, most EU countries have burgundy passports. The UK had burgundy passports while still in the EU.
Parts of the UK right wing press and politics stirred up drama about the colour of UK passports during the Brexit debate bemoaning that the dirty, unelected, bureaucratic EU had forced the beautiful, strong, innocent UK to switch from our nationally loved blue passports to their disgusting red ones when we joined the EU.
What really happened is the EU agreed (with UK input) on a standardised layout and design for passports. They did this to make movement around the EU easier and simpler. These agreed standards were guidelines. Each EU member was free to ignore them if they wished. Most use the standard because it makes their life easier. The UK chose to follow the standard, partially because it was one of the designers of the standard.
Because there was a standard colour (burgundy), this meant there was a higher demand for this colour. Higher demand means passport manufacturers prioritise their production for these demands. Prioritised manufacturing meant this colour and style became cheaper. It's not bespoke, it's the standard.
Because the Conservatives and Reform, etc. (the Brexiters) made such a big deal about the colour of UK passports, when Brexit happened they of course had to follow through on changing the passport colours. The result is that UK passports cost more to manufacture now than they did before, and last I checked were manufactured by a company in France! But the Brexiteers believe they've won against the EU by having blue instead of red passports.
Only the very old ones were blue - only people born before ~1970 (54 years old) would have ever used one as an adult, though people in their late 30s or 40s may have seen someone else using one as recently as 25-30 years ago.
For the majority of Britons, a traditional British passport is burgundy, like it's always been, and the blue ones are new "special racist passports".
[Edit] in answer to the original question, one of the terms of Brexit was "we get our old passport colour back". The mere idea got Daily Mail and Daily Express readers frothing at the cock.
It wasn't a referendum on what color our passports were.
The government decides what our passports look like. They could totally change the look without us having to leave the EU. It's not as if there was some EU mandate that forced our passports to be burgundy.
It's fair to say a big deal was made over the change in colour back when they announced it. But four / five years on from that it's only ever brought up by Remainers, constantly...