Titanium:
Burls
Litespeed
Moots will be over budget
Call me a snob, but I wouldn’t be riding Planet X, Lynskey or VN for your budget. With £3K, I’d personally go for the Pegoretti and a relatively cheap build of 10 speed Centaur/105 groupset and reasonable factory wheels from Campag or Shimano. What sort of riding do you want to use it for?
Funny how reputations come and go. Are you aware that the Lynskey family were Litespeed – established the brand’s reputation it still still trades on today (using the same family owned fabrication facilities that are now used for Lynksey), then sold off the name to ABG and started over under their own name? From a ‘snob’ perspective surely a family owned ‘niche’ brand has more kudos than a brand name operating under a larger multi brand name corporation?
Personally think the OP needs to give a little more detail about what they want from the bike other than what it’s made from and that it’s for use on tarmac. Racing, touring, audax, commuting, cargo….. or a mixture of the above. Steel and ti can be formed into very different feeling and performing frame – the Litespeed Blade TT frame I used briefly was an absolute bone shaker in comparison to more compliant Alu and carbon frames I’ve used for similar functions, which conflicts rather with the perceived wisdom of bikes of these materials ‘feel’ like.