Almost every fine art auctioneer will give you a valuation free of charge. (Of course they're hoping that you'll sell through their auction house but there's no commitment involved. I've taken items into Bonham's in London, with no appointment, and asked for valuations on them. Within minutes I was seen by the same guy that people queue for hours to see on the Antiques Roadshow).
However, assuming that the 'Wm Milne' in question is the Edinburgh artist of that name, this gallery is asking £3500 for one of his works:
http://www.richardtaylorfineart.com/artist/william-milne/twilight
That doesn't mean that anyone will be prepared to pay that though. I note, as well, that the provenance for the work is given as 'Christies'. That suggests that the gallery which is now offering the painting for sale might well have bought it there. Knowing the types of mark-up that galleries aim for, I'd guess that they would have only paid between £1000 and £2000 for it, so that might offer some sort of guidance as to what you could get at auction. (You'd then need to deduct the auctioneer's hefty commission from that figure, together with the VAT on the commission, perhaps leaving you with between £800 and £1600).
Those figures should only be used as VERY rough guides though, as the theme of a painting, its condition, its size and whether it's an early or late work by the artist can all make a big difference to its value.
As I've suggested already, take it to a reputable fine art auction house (not a general auction room) and ask for an estimate. Most auction rooms don't make any charge. (The only exception to that is if you require a formal written estimate for insurance purposes).