[4] In April 1959 he reached the final of the Scottish boys' championship at North Berwick, losing 3&2 to Hugh Stuart.

[5] Later the same month he won the Carris Trophy beating Peter Jochums from Germany, in a three-hole playoff after they had tied on 152.

[12] Returning to Britain he led the Coombe Hill Assistants' Tournament after two rounds but a poor finish left him tied for 5th place.

[15] In April 1963 Walker was runner-up in the Schweppes PGA Close Championship at Royal Birkdale, two strokes behind Peter Butler.

[16] In 1964 Walker won the Scottish Professional Championship for a second time, at Machrihanish, winning by two strokes from Eric Brown.

[18] From 1965 Walker had a number of less successful years, although he did finish tied for 43rd place in the 1966 Open Championship at Muirfield, despite a final round of 80.

[20] In August he won the Cutty Sark Tournament at Haggs Castle, two strokes ahead of Eric Brown and collecting the first prize of £200.

In August he won the Scottish Uniroyal Tournament.at Bruntsfield Links, by two strokes from Doug McClelland and taking the £400 first prize.

[23] Later in the month he reached the semi-finals of the Long John Scotch Whisky Match Play Championship at Moor Park, losing to Tommy Horton.