I live in the UK and got most of my parts from DigiKey in the US, including the case (in hindsight I probably chose the wrong one, but there are a lot of options out there). I also looked at Bluebell Audio in Scotland, for instance - they stock alternative cases as well as other things. I did not consider the Lansing case - maybe another error, but lots of builders appear not to use the Lansing one.
The advantage of using DigiKey is that the the manual has the DigiKey part numbers and also DigiKey will sell the right quantity of parts in most cases. Often suppliers in the UK appear to want to sell a minimum quantity of a particular part, say 50.
You may find that some of the parts shown in the manual have been replaced - you can get loads of advice on suitable replacements on this forum.
Watch out for out-of-stock parts - these can take a while to come through, but if you are building as slowly as me that may not be a concern. If you're in a hurry, you might want to look at an alternative part.
I used the 'stock' parts in the main - I did not use Auricaps for instance - expensive here in the UK. I also wanted to build it 'stock', get it working and then 'upgrade' later, if the mood took me.
I got the odd part from HiFi Collective - phono sockets, for example, and bits of hardware from my local store. When I built the Bugle, I got lots of parts from Maplin.
I got my tubes from Hot Rox in the UK, but I can't really advise on whether what I have is in any way 'the best'.
Good luck
John