Adoption in the UK can be done from my understanding using two different methods. The first method being going through your local council’s adoption agency or a voluntary adoption agency, you can also go through private agencies who’s process varies. To adopt the child has to be under the age of 18 and both parents have to agree unless they can’t be found, they are unable to consent or the child is at risk. You have to be in the UK for a year and have a permanent UK residence in order to be able to apply.
In order to start you contact the chosen agency who meet you and then if in agreement give you a form to apply which process normally is 6 months. For the application you have prep classes, several home assessment to check suitability, police check, give 3 referees and have a full medical examination. Once this is done there is then a panel meeting with all collected information to either approve or deny your application. If successful they then match you with a child, if not you can appeal the decision if necessary.
When you finally then have a child for up to 10 weeks you have to apply for a court order which gives all the parental rights to you. You can’t apply earlier than this and once complete the adoption is permanent. This gives you all the rights any parent would have and replaces their birth parents rights.
I hope you have found it useful to have a rough idea of what to expect and if more information is needed check out government web pages and do some research of your own by all means.