Last year's entry, 'Flying The Flag' by Scooch, finished 22nd out of 24 in the contest. Other recent poor showings include Daz Sampson's 'Teenage Life' and Jemini's 'Cry Baby'.
The last time a UK song reached the top ten in the competition was with Jessica Garlick's 'Come Back' in 2002.
This year's British contestant Andy Abraham is a 66-1 outsider with bookmakers, despite winning the public vote in March with his track 'Even If'.
Speaking about the recent downturn in the UK's fortunes, Wogan told the Radio Times: "If we finish nowhere again, I worry that disenchantment might take hold.
"Eurovision is such silly fun, and I love doing it, but if the enthusiasm isn't there...This year is pretty crucial for me. Eurovision without Royaume-Uni would be unfortunate."
Wogan was criticised by Eurovision organisers earlier this month for his lighthearted take on the singing contest.