unpaid rent and deposit

Rent Arrears

We have a tenant that we have been very patient with.
They have been in our property for nearly 10 months and although they have paid some money they have never paid the deposit so I could not put this into a scheme nor have they paid the monthly rent in full. They now owe in the region on £2500. They make lots of promises but fail to keep them. To make matters worse they have recently had a baby so we now expect no future payments at all.
Is section 8 the way forward to begin getting them out and does it matter about the deposit. We have bank statements to show exactly want they have paid and a completed tenancy agreement.
Can someone please advise. This was our 1st attempt at letting so next time I will get the deposit prior to them moving in.