Blair has not been good at grguing the UK's corner.
From the RN website:
Future Aircraft
The MOD considered all other options very carefully before selecting the JSF as the preferred aircraft for its new aircraft carriers. The other options included a marinised version of the Eurofighter (232 Eurofighters are ordered for the RAF) the American F18E, the French Rafale and an updated Harrier. But the Short Take Off and Vertical Landing (STOVL) variant JSF emerged as the best option.
Perhaps this has something to do with the fact that Rafale will be ready much sooner than F35B, or is partly to try to persuade the US to make more concessions on technology transfer.