Why are there not more peregrines in UK?

Why are there not more peregrines in UK given the abundance of their food and potential nest sites on buildings? The numbers of wood pigeons have risen sharply and they must be easy to catch but are they just too big and bulky to deal with?

Wood pigeons are taken. RSPB says.

Well their numbers are not increasing anything like fast enough in England as there were 8 wood pidgeons on my allotment this evening while I was on it. Some were bouncing up and down on the nets over the brassicas trying to peck the leaves and others after the fruit and indeed anything else they could consume.
The red kites increased very rapidly, suspect there are at least 4 that fly over the allotments and now see them frequently in many parts of England but peregrines still uncommon.

I have always assumed that top predators are controlled by Nature. Too many predators - too few prey items.
I looked for some science but found little
“_Researchers have traditionally assumed that the densities of the largest of predators are determined by the availability of their prey supply, but recent studies seem to contradict a bottom-up contr_ol.” is from a recent study of large carnivores like lions and wolves,
I could find no specific references to (peregrine) Predator/Prey ratios. But there is plenty about their breeding ratios Urban/Rural and there are references like “Prey species diversity was lower in urban environments, supporting findings from other studies that bird diversity tends to decrease with urbanisation (e.g. Blair 1996; Clergeau et al. 1998;.…” to be found.
It’s all very well not seeing a Peregrine very often and seemingly being plagued by pigeons - but that’s not science. Where’s the science?

Is an interesting thing. There is a niche for them which was waiting until they were reintroduced, that might apply to the Sea Eagle too. Peregrines have always been here and their special niche is perhaps full.

Red kites hung on in Wales at a very low population size for many years before the population reexpanded.

After 50 years there’s still not a great number of ospreys in Britain, and only 100 pairs of sea eagles.

Kite numbers kept down by persecution (they are very easy to kill with poison bait). Ospreys are migratory and I think quite tightly tied to close to ‘home’ nest - now they are trying to get them to nest in England and they might start to expand quite quickly but of course they also need suitable prey in water. Sea eagles also have an issue with prey and possible persecution.
Whereas peregrines have an abundance of prey and nest sites and I don’t think they are being persecuted, may ask BTO for comment on this.

The popular press has stuff. https://www.dailymail.co.uk/news/article-5466089/Peregrine-falcon-numbers-record-high-British-towns.html and https://app.bto.org/birdtrends/species.jsp?&s=pereg
I am still unclear of what you are asking. If you see a peregrine it will have a huge range and will drive off all other competitors. One for a City centre is all you’d get, despite pigeon over-crowd.
Kites are gregarious (like crows), ospreys are very tolerant (Kielder Ospreys) - peregrines really like their own company.
I think you’d be lucky to get two in a small town. My memory of North Wales’ ‘wilderness’ suggested one per valley at the most. One in Cwm Dulyn say and the next one on Black Ladders, perhaps the next on Gallt yr Ogof - in fact that was precise when I was there and some years with only two of those,

Kites, when reintroduced, were fed at (volunteer?) feeding stations for many years, so they were helped to become established. I don’t think peregrines would take to that.
We have a pair of peregrines that nest in Bristol Gorge. I think there’s only ever one pair at a time…I’ll check.

These two sites are about Bristol peregrines