Thanks for reply.
It appears that overall you have been in UK for around 15-16 yrs already. Your submitted your application earlier than the regular 14 yrs required for which UKBA should credit you. The fact that they have taken 4-5 yrs to process is not your fault but it has resulted in you going beyond the 14 yr mark. Delay in processing is not a novelty for UKBA. I had a long residence case which was not decided for 7yrs and we had to chase through MP to get any response.
If you have not already done so, you should send UKBA supporting letters from employers, friends and family to confirm that you have indeed been in UK since 1994. Details of your relationship with family in UK and strength thereof.
The human rights angle which needs to be highlighted if not already done so. This is where you should send supporting letter from your partner detailing your relationship (when met, any cohabitation, photographs together, how child is being brought up etc) and birth certificate for your child. Common law marriage is not a concept accepted in the UK. However, you are unmarried partners and your relationship should be credited for its longevity thus far.
Ideally, you should give a variety of evidence for each year of your residence in UK since 1994 eg school certificates, official letters such as covering letter for national insurance card, utility bills, P60s, P45s, bank and credit card statements, tenancy agreements etc.
This is your application and it is up to you to provide the evidence to UKBA. If you can prove that you have strong ties in the UK and you are not a threat to society at large, it will be difficult for UKBA to justify refusal. They may do it any way but you should have a right of appeal before an independent Immigration Judge. On the face of it, your case looks reasonable and your solicitor should be able to advise you further.