Beebase is the website of the National Bee Unit, they are (indirectly) part of DEFRA, so as near to official estimates you are likely to find. Regional inspectors produce annual reports which vary in detail but give some idea of what they use as working totals.
https://secure.fera.defra.gov.uk/beebase/index.cfm?pageid=168
Number of beekeepers registered to BeeBase 31047
Beebase average colonies per beekeeper 4.43
Total number of colonies 31047 x 4.43 137538
That's England and Wales quoted in the SE Honey Survey at the end of 2013. Registration is voluntary and aimed at disease control. Working assumptions elsewhere in reports are that the estimated actual numbers are 20% or 25% over that figure. There are unregistered hives, also registered but given up. Scotland and NI you'd have to look elsewhere or multiply in some proportion.
BBKA claim 24,138 members as at 30/9/2013 in the finance papers for the 2014 delegates meeting. The papers may be in a members controlled area of their web site. Membership is overwhelmingly though local associations. However, not all beekeepers are members of associations and not all associations are members of BBKA. Basically England this time with a few outside. Wales, Scotland and NI have separate records.
Membership of BBKA probably best approximates overall trends in England beekeeper numbers, search for the_history_of_the_bbka_1306180988.pdf on the BBKA website. Best guess is that the peak was around 1953 with 80,000 members (not always recorded centrally). Membership dropped to under 9,000 in 2001, a combination of steep falls when sugar rationing ended, long term decline and new set backs such as varroa mites. Several long standing suppliers closed or merged towards the end of the period. From there increasing interest saw numbers rise steadily but churn (beekeepers giving up after a year or two) and fewer starters suggest numbers have plateaued in the last year or two at around 24,000. Outside England the UK pattern is likely to be similar. Beebase is not a reliable source of trends because registration has been campaigned for in recent years.
There is also the Bee Farmers Association who represent professional and semi professional beekeepers - qualification is 40 or more hives. In round numbers around 300 members across the UK ranging up to the largest operation with 2000 plus hives. Their numbers should be included in the Beebase registered totals. Many are BBKA members too for their own reasons.
Hive types are harder to estimate, suppliers are not free with information on what they sell. No idea how reliable it is but I have heard estimates that more than 80% in use are wooden National if you include variants like 14x12 and a few Rose. That seems reasonably consistent with what you see around association apiaries. Hives last 20 years or more and keeping spares for one pattern is far easier than multiple types so changes are slow.
The rest are very varied.
- High density polystyrene National are increasing in numbers, at least 4 or 5 patterns are actively marketed. Nucleus box versions have been far more frequently seen.
- The largest supplier of wooden hives claim WBC is still their second best selling model after National and they are popular as garden features.
- Commercial were perhaps more popular than they are, some used the broods with National supers and they could be losing out to 14x12 National for those who like the larger brood frame.
- In addition to small scale Langstroth users there are larger bee farmers who use them because that is the overwhelming pattern worldwide and they can shop around for bulk suppliers.
- I have seen Smith use estimated at 3% of total UK hives, I think that was based on frame sales.
- Must be some Dadant out there because the suppliers list frames for them, although hard to estimate because as with Langstroth there are imports.
- Various top bar, long designs or Warre types are home made or bought in.
- There are "patent" designs such as Omlet/Beehaus or Apimaye but advertising and other publicity probably makes them more prominent than the numbers actually in use.
- Designer variants are sold complete or as plans such as Dartington and Hedgecoe.
- Exotica like Sun hives are used by a few.
- There will even be a few museum pieces still in use such as Cottage or Gale and I know of some personally imported "long hives" from Eastern Europe.
On a wider scale, there have been recent EU sponsored data collections which result in surveys of beekeeper numbers like this one
http://www.plosone.org/article/info:doi/10.1371/journal.pone.0079018 which suggests 620,000 EU beekeepers.
