At that price point you’ll struggle to find much that’s worth having. I think that Mahalo do something but IIRC the particular models are best avoided - I’m not a Uke snob and have an old Mahalo U30 Soprano that I love.
I played a Makala Concert for a while (my second Uke) and was very pleased with it. IIRC I didn’t replaced the nut on that one but have made new nuts from bone blanks for a few Ukes, when I make a nut I space the string slots wider apart and that’s really helped me.
Baton Rouge (spelling?) do a couple of wider neck Ukes and they are borderline on the OP’s budget. After that Islanders are wide necks but approaching double the OP’s budget. I have an as new Concert Islander that I keep meaning to post on eBay, they’re good but I mostly play Soprano.
An elderly friend of mine has a well set-up Aria Concert gathering dust (she prefers Soprano) and that had wider (than normal) spaced strings, in normal times I’d put it on eBay for her but we’ve not met since March ‘20. It would have been a good starter for the OP.
There’s a few alternatives around, perhaps a second hand Makala Concert might turn up somewhere. If you have a good span on your hand then consider a Tenor too.
Posting on here can prove difficult. Always copy your text to the clipboard before posting.
Thanks a lot for such a detailed reply, Graham. Even though you warned me I still managed to fall foul of the Forum posting curse! Hey ho. Let's try that a second time...
I actually considered quoting a post of yours about the Mahalo I think you're talking about - in this thread here:-
https://forum.ukuleleunderground.com/showthread.php?117190-Mahalo-2500-Kahiko-Soprano-REVIEW
I came away from Barry's review with the same impression that you initially had - that with a string change, the Kahiko might be a decent little budget option. That was appealing because they do a Mahalo MK1PWTBR M1 Kahiko Plus Wide Neck Soprano which is available for GBP20 making it a really wallet-friendly option.
The posts between you and Barry put me off that idea!
I think I may have found a good alternative though...
I have a HanoHano long neck soprano that has a super wide fretboard and is very easy to play. Picked it up for $80 in a music store and it even sounds great. They share office with Leolani brand that also makes a long neck soprano and may be easier to find.
Thanks a lot Merlin. They look nice, but (as I think you may have suspected in giving me an alternative company name to search for) I can't see either companies' ukuleles available in the UK.
Beuatiful but beyond my budget at this moment in time, unfortunately!
I think I've found a good option though...
Flight's "Natural Series" NUT310 Tenor has a nut width of 38mm. I just took delivery of a Flight NUC310 Concert (which came up in a very good deal and which I bought with a view to giving to our children to practice on. Now it's arrived, it's far too nice to let them abuse!) It seems really well made and (to my subjective eye) is really nice to look at. The Tenor is reduced in a local shop - currently GBP65 - and that seems to meet all my criteria...
EDIT: I've just found that quite a lot of Flight's models have 38mm wide nuts, including their Natural Series NUC200 Concert which can be had for GBP40.
The 200 range is a bit more basic than the 310 range - it is made from laminated teak (as opposed to laminated sapele on the 310), the bridge and fretboard are Nandu (as opposed to walnut) and the nut and saddle are PPS (as opposed to bone) but in terms of hitting the brief the NUC200 looks like it ticks all the boxes and has to be the frontrunner.