We'll get there

try this:
SELECT Member.Forename, Member.Surname, Event.Gender AS Gender, Event.Age AS Age, Event.Distance AS Distance, Event.Stroke AS Stroke, Venue.[Name of Pool] AS VenueName, Times.[Date] AS DateofEvent, Times.Time AS TimeRecorded
FROM Member, Event, Times, Venue
WHERE Member.[Member ID]=Times.[Member ID] And Event.[Event ID]=Times.[Event ID] And Venue.[Venue ID]=Times.[Venue ID]
AND Times.Time = (SELECT Min(Times.[Time]) FROM Times WHERE Times.[Member ID] = Member.[Member ID] AND Event.[Event ID]=Times.[Event ID])
GROUP BY Member.Forename, Member.Surname, Times.[Date], Times.[Time], Venue.[Name of Pool],Event.Stroke,Event.Gender,Event.Age,Event.Distance;