Hello Ruth
Yes carrots are versatile and June is excellent for large roots to store, then the first half of July allows time for smaller roots to eat from September, and it is good to sow an early variety in July such as Early Nantes.
I would say that slugs can happen at any time and I lost a June sowing last year which I intersowed between garlic, whereupon it just rained non-stop, whereas the early March sowing, which was a gamble really, grew best of all after getting away in that lovely warm, dry March, helped by fleece laid on top. Carrrot seed is not too expensive (avoid hybrids!) and an undug bed should be always weed free, so it is worth trying a few extra sowings.
Incidentally my June sowing in bare soil came up well last year and the carrots are delicious now, from storing in a sack with some soil on the roots.