cant help u with UK process in detail, but its very similar to US
basically you have to get a homestudy done, i think in UK its free and a service offered by the local council.
homestudy with the social worker takes about a dozen visits
here is more info.
The adoption process and where to get support : Directgov - Parents
if u are looking to adopt from a different country, then u have to deal with more paperwork in UK as well as in that country