When you do approach it, make them aware that you will use your holiday entitlement for any time off so they won't think you will be expecting to have this off for 'free'. Explain that while pregnant women get time off for antenatal appointments, in adoption you don't (which is really unfair). A lot of companies are really good, will let you make up the hours etc, but if your boss isn't compassionate they may do things 'by the book'. Each appointment might also be for 2-4 hours, and there will be several you have to have over 6 + months.
Also make them aware that once you are approved it could be months before you are matched. I mean it might not be, but it could be. I think a lot of employers panic and think that once you are approved you will be matched straight away! So with the time it takes to get approved, plus (potentially) time to get a match, you may not be leaving for a year! I guess it's making them aware of that so they don't panic, even though you know it could be shorter, but it also might not be depending on the child/children you are looking for.
Once matched, you are then legally allowed 5 days for 'appointments', which could be to meet the paediatrician or for intros. I think it's for 6 hours per day but most companies let you have the day off. They are legally obliged to pay you for this time off.
Then you need to find out the company adoption policy.
Is it standard or enhanced?
What is the maternity policy, does it match the adoption policy (it doesn't have to, unless they once were and one was changed and not the other)?
The size of the company might also matter, an SME may not even have an adoption policy, but legally they have to have one. Even in large national companies adoption still isn't a regular thing, and I was shocked at how little some HR departments knew about it!
I would go with as much information and facts as you can, try and preempt any questions or issues they might have, and be really really positive and happy about it (it's hard to be horrible to someone if they're being nice to you!).
Also, how long have you been in your job?