The dentist murdered a cousin in Halifax where the motive wasn't revenge or love (clue 3), an inheritance (Brighton, clue 1) or power (solicitor, 5), so blackmail. The revenge killing wasn't in Fishguard or Dunoon (2) so Grantham. The love-motive murder wasn't (4) in Fishguard, so Dunoon, thus the motive in Fishguard was power. The artist's motive was an inheritance (1). The partner (2) was murdered for love by (4) the plumber. The butler killed for revenge. The sister (4) was murdered for revenge. The friend wasn't (5) the victim of a power struggle, so inheritance. The power motive involved the murder of the mother.

Thus:

Artist - friend - inheritance - Brighton;

Butler - sister - revenge - Grantham;

Dentist - cousin - blackmail - Halifax;

Plumber - partner - love - Dunoon;

Solicitor - mother - power - Fishguard.

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