Fennel

Difficult to tell, they obviously look very leggy and that is probably not good!  But i do remember growing fennel one year and coming back after i'd planted them out to find they d all been nibbled to nothing, I left them and lo and behold they came back and thrived so perhaps the answer might be to cut them back and see what happens?

Yes, Florence fennel. 

Have been told to try planting deep?

Not at all sure what's happened to your plants, but in any event neither Florence nor herb fennel takes kindly to transplanting, especially at that size.

It is inclined to bolt if sown too early - I'd recommend starting again by sowing directly outdoors in your chosen growing position (I don't sow mine until mid-June so plenty of time, although some varieties are more suited to sowing earlier than that.)

Wot he said ! Also it is a nice bit of stuff to have for the salad or to roast but I found the problem is it does bolt very quickly once it bulbs, so if you grow a row of it be prepared to either scoff loads of it or have to put some on the compost heap... it also does not like being thirsty. I think the best way to grow it is to prepare a nice deep row which is weed free and well enriched with compost and manure. Then station sow three or four seeds every 200 - 250 mm once they are away you can take out the ones you don't need.