Yes Charlotte they should be ok. Could always get your guest to 'harvest' your crops might get them too grow there own lol

Lettuce and radishes yes but your carrots are likely to be rather small, but by June you should be thinning them anyway so use the thinnings - it will also depend on when you planted them as everything is late this year. If you look on the back of your seed packets it will tell you when to expect to harvest. You can also visit
http://www.gardenorganic.org.uk/growyourown/Vegetables-complete.pdf

which gives good clear information on when to sow and harvest - large pdf so can take a while to download