Syed (Foxford School and Community College, Coventry) has supplied a diagram of a solution:
Joshua (Brooklands Primary, Suffolk) explained his thinking well:
From clue 1, two girls sit next to each other, and from clue 4, Carol did not sit beside Annie or Ellen - so Ellen and Annie must sit next to each other. From clue 5, Felix sat opposite Ellen.
From clue 2, David sat opposite Bert, so I put them on the two ends of the table. Which means Carol sits next to Felix - which fits in with clue 3 (Felix sat to Carol's left).
Samantha (Nanyang Primary School, Singapore) realised that Bert and David could swap seats and still fit all the clues.
Josh (Ampthill, Bedfordshire) gives an excellent description:David is sat at the left end of the table and Bert is sat facing him at the right end.
Sally (Tattingstone Primary, UK) thought about the problem in a similar way to Josh.
Jason (Lark Rise Lower School, UK) was the only one to send in a different, but similar, seating arrangement: