I'm new to gardening and decided to try my hand at growing some veg, using an old bed base as a little box garden to start.

So far everything is great except for a rookie mistake and that was not leaving enough space between my broccoli, cauli and cabbage. My other mistake was not separating my carrots so at present I have bunches of them growing together, I took one out the ground the other day and the carrot is about an inch and a half long, tastes great but I'm worried that they'll not grow as well, being squeezed together like that.
My question is:

Is it now too late to try and transplant them or can that still be done without killing them?

Thanks

Can be planted out if you are careful and try to keep as much root as possible on each plant. They will need watering because this is the hot season and they could dry out because the roots will take time to establish their proper intimate contact with the soil.

Thanks for that reply, what's the best way to do it, wasn't sure whether to dig a fair chunk around them and a bit deeper then put them in water to break up the soil but leave all/most of the roots before planting, is that ok or is it a case of pulling them out as if using them and trying to re-plant from there?

Thanks for your help with this!

Big chunk then water to separate is good. If you just pull you will damage the roots too much and they will not re-start.