Very simply, the gain is first reduced by indexation and taper relief. Indexation only applies for assets bought before 17 March 1998. This is a little complicated so i won't divulge further. as it won't apply in your case.
Taper relief is then applied. In you example you get 6 years taper relief- that is only 80% of the gain would be chargeable. In your case therefore only �28,000 would be chargeable.
The annual allowance you talked about is then taken from this figure. The annual allowance in question is the figure when the asset is sold. This year it is �8,800. Therefore your total chargeable gain is �19,200.
This is then added to your income to calculate the tax due- i.e. if you pay at the higher rate it is taxed at 40%, basic rate 20%, lower rate or nil rate 10%. If it spans two tax bands, i.e. basic rate and higher rate, you pay part of it at basic rate and part at higher rate.
Hope that is clear?