Roots in my greenhouse

I would really like some help as I'm new to growing veg and I can't seem to find the information I'm looking for online.
Last year I grew tomatoes / cucumbers in my greenhouse. The cucumbers grew really well not so many tomatoes but enough for the two of us.
The soil I have in the greenhouse is just full of little roots. I've tried getting them out which I must say is rather hard work but I'm willing to do this if they need removing.
My questions are....
Do I have to get rid of them all?
Can I just top up the soil and try and dig it in, not easy as they are spread throughout the soil?
Any help would be great.
Thanks in advance

It may be easier to grow cucs and toms in plastic buckets and potting compost rather than in the beds. The beds can build up diseases over the years and therefore need digging out and the soil replacing on a regular basis.