Broccoli?

I have what I think is Purple Sprouting Broccoli growing in my garden, I planted it last April from plants I was given by my brother-in-law who said they were cabbage.
The cabbage was destroyed by caterpillars, and I thought I'd just leave them there until this year and then re-plant new one's, but these (see photo's) started to grow?
I've left them until now to see if they are Purple Sprouting Broccoli and if so, will cut them and cook them.
A couple of questions please:-
If I cut the purple shoots and leave the plants as is, will more purple shoots grow or should I then remove the plants altogether?
I don't know what the other stubby plants are, any ideas? or should I just dig them up?

 

Looks like purple sprouting to me, mine is just starting to crop.

You should be able to see the undeveloped shoots on the plant these will continue to develop when the bigger ones are picked.
I'd remove the stubby ones.

 

Thanks for that, I'll do as you suggested.

 

Looks like its a bit far gone to me and should have been picked earlier, it often starts to bolt if we get a warm spell.