So taking your query, I just changed the order in the ORDER BY clause so LATEST_TAKEN was the first sort parameter. Then I added a LIMIT 1 so it only returned one result. I think this should return what you're looking for
SELECT
    Bfinf_other_150126to150201_150204124439.*
FROM
    Bfinf_other_150126to150201_150204124439
WHERE
    (((Bfinf_other_150126to150201_150204124439.FULL_DESCRIPTION) Like "English Soccer/Barclays Premier League*") AND
    ((Bfinf_other_150126to150201_150204124439.LATEST_TAKEN)<[DT ACTUAL_OFF]) AND
    ((Bfinf_other_150126to150201_150204124439.SPORTS_ID)="1") AND
    ((Bfinf_other_150126to150201_150204124439.EVENT)="Correct Score") AND
    ((Bfinf_other_150126to150201_150204124439.IN_PLAY)="pe"))
ORDER BY
    Bfinf_other_150126to150201_150204124439.LATEST_TAKEN DESC,
    Bfinf_other_150126to150201_150204124439.EVENT_ID,
    Bfinf_other_150126to150201_150204124439.FULL_DESCRIPTION,
    Bfinf_other_150126to150201_150204124439.SELECTION
LIMIT 1;
I have simplified matters for clarity:
SELECT   
Bfinf_other_150126to150201_150204124439.FULL_DESCRIPTION, Bfinf_other_150126to150201_150204124439.SELECTION, Bfinf_other_150126to150201_150204124439.ODDS, Bfinf_other_150126to150201_150204124439.LATEST_TAKEN
FROM Bfinf_other_150126to150201_150204124439   
WHERE   
(((Bfinf_other_150126to150201_150204124439.SPORTS_ID)="1") AND ((Bfinf_other_150126to150201_150204124439.EVENT)="Correct Score") AND ((Bfinf_other_150126to150201_150204124439.IN_PLAY)="pe") AND ((Bfinf_other_150126to150201_150204124439.FULL_DESCRIPTION) Like "English Soccer/Barclays Premier League*") AND ((Bfinf_other_150126to150201_150204124439.LATEST_TAKEN)<[DT ACTUAL_OFF]))  
ORDER BY    
Bfinf_other_150126to150201_150204124439.EVENT_ID, Bfinf_other_150126to150201_150204124439.FULL_DESCRIPTION, Bfinf_other_150126to150201_150204124439.SELECTION, Bfinf_other_150126to150201_150204124439.LATEST_TAKEN DESC; 
Gives:
FULL_DESCRIPTION    -    SELECTION   -   ODDS    -   LATEST_TAKEN  
English Soccer/Barclays Premier League/Fixtures 31 January  /Hull v Newcastle   0 - 0   9.2 31-01-2015 12:34:52  
English Soccer/Barclays Premier League/Fixtures 31 January  /Hull v Newcastle   0 - 0   9.8 28-01-2015 03:09:13  
English Soccer/Barclays Premier League/Fixtures 31 January  /Hull v Newcastle   0 - 0   10.5    25-01-2015 19:19:35  
English Soccer/Barclays Premier League/Fixtures 31 January  /Hull v Newcastle   0 - 0   9.4 24-01-2015 11:51:58  
English Soccer/Barclays Premier League/Fixtures 31 January  /Hull v Newcastle   0 - 1   9.2 31-01-2015 12:45:05  
English Soccer/Barclays Premier League/Fixtures 31 January  /Hull v Newcastle   0 - 1   9.6 31-01-2015 12:00:57  
English Soccer/Barclays Premier League/Fixtures 31 January  /Hull v Newcastle   0 - 1   9   31-01-2015 11:50:25  
English Soccer/Barclays Premier League/Fixtures 31 January  /Hull v Newcastle   0 - 1   8.8 30-01-2015 18:26:06  
English Soccer/Barclays Premier League/Fixtures 31 January  /Hull v Newcastle   0 - 2   16  31-01-2015 12:45:05  
English Soccer/Barclays Premier League/Fixtures 31 January  /Hull v Newcastle   0 - 2   16.5    31-01-2015 12:43:22
I require rows 1,5 and 9
I.E. For each match (FULL_DESCRIPTION) the correct score(SELECTION) ODDS at the greatest time (LATEST_TAKEN) before the start of the event ([DT ACTUAL_OFF).