Every maker has their own lasts, sometimes many of them from the same line. Until you know one that fits you well, guessing can be a nuisance. I even have two pairs in different sizes on the same last (oxford versus derby) because they are just made differently. But generally, if an oxford on a particular last fits you well, then you can go back to it time and again for any shoe you want with a reasonable degree of confidence.
Anyway, it seems you don't have one in mind yet. Regarding the suggestions above, EG etc. is probably out of your price range (mine too!) unless you find an eBay bargain or visit an outlet. But just in case, then I found the standard "E" fitting narrow from them too, on the 888 and one other I can't remember.
But, from my own more modest experience:
Church's traditional 73 last is pretty slender, and there are still some available.
Cheaney's lasts are quite sleek and narrow too in standard form: the 2003, and I think it's the 11028.
All of those are available for well under £400 if you shop around, and from my personal experience (in my case needing a wide fitting in either), Cheaney make fantastic quality shoes for around the £250 mark, including VAT. Check out Herring, who stock both of the above among others, including several Cheaney-made models in their own name, that I can personally attest are excellent.
More to the point, if you email a question or ask it on their Facebook page, they are very knowledgeable about the brands they stock, and bend over backwards to help find you something suitable. I've bought several pairs of shoe through them, and go back because the website is easy to search by size, and I know their service and support will be there if I have a question.
N.B. At the risk of sounding condescending if you already know this: different makers use different letters to designate their width fittings: in the UK, "F" normally means standard, and "E" would be narrow. This is true of Church, Cheaney, Barker, Loake, Alfred Sargent, and many others. But some, especially the higher-priced brands like John Lobb, Edward Green,Gaziano and Girling, and also Crockett and Jones, use "E" as their standard, so for them "F" is wide (or EE for John Lobb). Tricker's use numbers, just to be individual. Americans have a different system altogether, with "D" usually the standard. So check with each maker what their "narrow" fit is, if they have one - it's easy to get muddled up, and I have bought the wrong one at least once.
Which reminds me: maybe buy American? I guess it's a matter of market scale, but Allen Edmonds for one, and possibly others, sell shoes in a huge range of sizes, from extra extra narrow up to extra extra wide. For what it's worth, I find their standard width generous across the toes, but shallow over the instep. Anyway, check them out as they're mostly within budget (although stupid shipping costs don't help), and they also have a printable size guide that I've found to be accurate. Good luck.