Moving Raspberries?

I have a very small garden, and one of my borders is given over to autumn fruiting raspberries, with a couple of tayberries and a blackberry thrown in. 

A couple of years ago, I bought some 'bush type' summer fruiting raspberries, which I have in pots and are doing quite well.   I'd much rather have a border full of these, as I'm sure the tayberries and blackberry would appreciate having a bit more space and light.

So, my question is:- Is it too late to dig up the autumn fruiting raspberries and give them away?  I'm not bothered about them fruiting this year, but wasn't sure if they'd have time to establish themselves elsewhere if they are moved?

AM