Most (not all) people who come to adoption come via way of years of fertility treatment followed by a time coming to terms with it not working.
I would say mid forties one of the more 'usual' ages to adopt and...(and this is key), depending on local authority/agency I would think that that age alone wouldn't rule you out of adopting a child who was quite young.
It certainly shouldn't be a barrier to adopting an older (4-5) child.
I know a lot of adopters through my agency. Most are 40s or older. Many are matched with babies or toddlers. As other's have said, there is no formal limit and practice varies a lot between LAs. Matching is also very personal, there's a lot of pot luck involved.
Assuming good health, I'd suggest hitting 50 it starts to be a bigger issue, you have to look at older kids; 55 and finding a successful match becomes more difficult, though I know people who've matched at this age.
It depends largely on health and how long a child would be dependent upon you. So if you're 30 and have a serious health condition you'd might be refused as they need to know that you hare going to be well and still around until a child becomes an adult. Alternately you might be in your late 40's and in great health so be low risk in terms of being around in 20 years.
Saying that some agencies operate differently, my circumstances are a bit unusual and I was assessed as a potential adopter for a specific child (still a baby at the time) by NCH although the child was 'looked after' so my case was still to be put before the local authority adoption panel not the NCH panel. I was 37 at the time and single. The NCH worker told me that if were being considered at the NCH panel I wouldn't be considered as a priority for such a young child but I would be ahead of lesbian and gay couples in the queue!
We adopted aged 33 and 37. We were told we were considered young for adopters as by the time most people had gone through fertility treatment they were more usually in their mid 40s. Both the LA we have adopted through had no upper age limit.
The Authority we adopted with told us that the age gap between the youngest adopter and the child should be no more than 45 years. They also told us that there were exceptions and that good health was the most important thing. At the time we assumed this was the case everywhere! We didn't look into it as this suited us fine.
I was 45 when we adopted our amazing, smart and gorgeous child aged one. That was nearly 3 years ago.